# Math 10 - Unit 5 Final Review - Polynomials

Size: px
Start display at page:

Transcription

1 Class: Date: Math 10 - Unit 5 Final Review - Polynomials Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Factor the binomial 44a + 99a 2. a. a( a) c. 11a(4 + 9a) b. 11(4a + 9a 2 ) d. 22a(2 + 9a) 2. Factor the binomial 15y 2 48y. a. 3(5y 2 16y) c. y(15y 48) b. 3y(5y 16y) d. 3y(5y 16) 3. Factor the trinomial 4 8n + 12n 2. a. 4( 2n + 3n 2 ) c. 2(2 4n + 6n 2 ) b. 4(1 2n + 3n 2 ) d. 4(1 + 2n + 3n 2 ) 4. Factor the trinomial 33b b a. 11(3b 2 9b + 7) c. 11(3b 2 9b 7) b. 33(b 2 3b 7) d. 33( b b + 7) 5. Factor the trinomial 24c 3 d 40c 2 d 2 32cd 3. a. 8cd(3c 2 5cd 4d 2 ) c. 8cd( 3c 2 + 5cd + 4d 2 ) b. 8cd(3c 2 + 5cd + 4d 2 ) d. 8cd(3c 2 + 5cd + 4d 2 ) 6. Factor the trinomial 42x 5 y 6 24x 4 y 5 54x 3 y 7. a. 6x 4 y 5 ( 7xy 4 9y 2 ) c. 3x 3 y 5 (14x 2 y + 8x + 18y 2 ) b. 6x 3 y 5 (7x 2 y + 4x + 9y 2 ) d. 6x 3 (7x 2 y 6 + 4xy 5 + 9y 7 ) 7. Factor the binomial 10m 2 40m 4. a. 10m 2 (1 + 4m 2 ) c. 10(m 2 + 4m 4 ) b. 10m 2 (4m 2 ) d. 5m 2 (2 + 8m 2 ) 8. Simplify the expression y 2 + 8y 6 9y 2 24y 26, then factor. a. 8(y 2 2y 4) c. 4(2y 2 + 4y + 8) b. 8(y 2 + 2y + 4) d. 4(2y 2 + 4y + 1) 1

2 9. Which expression represents the area of the shaded region? a. 2r(2r π) b. r 2 (1 π) c. r 2 (4 π) d. r(r 2π) 10. Expand and simplify: (p + 3)(p 7) a. p 2 4p 21 c. p p 21 b. p 2 10p 21 d. p 2 + 4p Expand and simplify: (4 r)(7 r) a r + r 2 c r + r 2 b. 28 3r + r 2 d r + r Factor: t 2 + 9t 36 a. (t 2)(t + 18) c. (t + 12)(t 3) b. (t + 2)(t 18) d. (t 12)(t + 3) 13. Factor: v 2 13v + 36 a. (v + 3)(v + 12) c. (v 4)(v 9) b. (v 3)(v 12) d. (v + 4)(v + 9) 14. Factor: 24 2x + x 2 a. (6 + x)( 4 + x) c. ( 3 + x)(8 + x) b. (3 + x)( 8 + x) d. ( 6 + x)(4 + x) 15. Factor: z + z 2 a. (42 + z)( 2 + z) c. ( 42 + z)(2 + z) b. ( 6 + z)(14 + z) d. (6 + z)( 14 + z) 16. Factor: 3b b + 18 a. 3(b 2)(b + 3) c. 3(b 1)(b + 6) b. 3(b + 2)(b 3) d. 3(b + 1)(b 6) 17. Factor: 4d 2 28d a. 4(d + 3)(d 20) c. 4(d 3)(d + 20) b. 4(d + 5)(d 12) d. 4(d 5)(d + 12) 2

3 18. Complete: (a + 6)(a ) = a 2 + a 12 a. (a + 6)(a 4) = a 2 + 4a 12 c. (a + 6)(a 2) = a 2 + 2a 12 b. (a + 6)(a 2) = a 2 + 4a 12 d. (a + 6)(a 4) = a 2 + 2a Factor: c 2 4c 117 a. (c 9)(c + 13) c. (c + 9)(c 13) b. (c 3)(c + 39) d. (c + 3)(c 39) 20. Factor: 12 4g g 2 a. (4 g)(3 + g) c. (6 g)(2 + g) b. (6 + g)(2 g) d. (4 + g)(3 g) 21. Expand and simplify: (h 6)(h + 11) a. h 2 5h 66 c. h h 66 b. h 2 + 5h 66 d. h 2 17h Factor: 5m m + 60 a. 5(m + 2)(m 6) c. 5(m 4)(m + 3) b. 5(m 2)(m + 6) d. 5(m + 4)(m 3) 23. Factor: 7n 2 14n 105 a. 7(n + 3)(n 5) c. 7(n 15)(n + 1) b. 7(n + 15)(n 1) d. 7(n 3)(n + 5) 24. Which multiplication sentence does this set of algebra tiles represent? a. (2x 2)(2x + 2) c. (2x 2 + 2x)(2x 2 + 2x) b. (2x 2 + 2)(2x 2 + 2) d. (2x + 2)(2x + 2) 3

4 25. Which set of algebra tiles represents 3x 2 + x + 4? a. c. b. d. 26. Expand and simplify: (6p + 3)(5p 6) a. 30p p 18 c. 30p p 18 b. 30p 2 21p 18 d. 30p 2 51p Expand and simplify: (8g 3)(7 3g) a. 24g g 21 c. 24g g 21 b. 24g 2 65g 21 d. 24g g Factor: 25x x + 16 a. (25x + 4)(x + 4) c. (5x + 4)(5x + 4) b. (25x + 8)(x + 2) d. (5x + 8)(5x + 2) 29. Factor: 16s 2 137s 63 a. (4s 7)(4s + 9) c. (16s + 7)(s 9) b. (4s + 7)(4s 9) d. (16s 7)(s + 9) 30. Factor: 48y 2 116y + 60 a. (16y 12)(3y 5) c. 4(4y 5)(3y 3) b. 4(4y 3)(3y 5) d. 4(4y + 3)(3y + 5) 31. Factor: 24b b 14 a. 2(4b 1)(3b + 7) c. 2(4b 7)(3b + 1) b. 2(4b + 7)(3b + 1) d. 2(4b + 1)(3b 7) 32. Expand and simplify: 3(1 2t)(9 + 4t) a. 24t t + 27 c. 72t 2 126t + 81 b. 24t t + 27 d. 24t 2 42t Factor: 7n n 15 a. (7n 1)(n + 15) c. (7n + 15)(n 1) b. (7n + 1)(n 15) d. (7n 15)(n + 1) 4

5 34. Factor: 4 9z 13z 2 a. (2 13z)(2 + z) c. (2 + 13z)(2 z) b. (4 13z)(1 + z) d. (4 + 13z)(1 z) 35. Factor: a + 30a 2 a. 5(4 + 3a)(9 + 2a) c. 5(4 3a)(9 2a) b. (20 15a)(9 2a) d. 10(18 1a)(1 3a) 36. Factor: 96w w 42 a. 6(8w + 1)(2w 7) c. 6(8w 7)(2w + 1) b. 6(8w + 7)(2w 1) d. 6(8w 1)(2w + 7) 37. Expand and simplify: (8h + 3)(7h 2 4h + 1) a. 56h 3 53h 2 20h + 3 c. 56h 3 11h 2 4h + 3 b. 56h h 2 12h + 3 d. 56h 3 32h 2 + 8h Expand and simplify: (5m 3n) 2 a. 25m 2 9n 2 c. 25m 2 30mn + 9n 2 b. 25m 2 15mn + 9n 2 d. 25m 2 + 9n Expand and simplify: (7m 2n) 2 a. 49m 2 4n 2 c. 49m 2 28mn + 4n 2 b. 49m 2 14mn + 4n 2 d. 49m 2 + 4n Expand and simplify: (7m 3n) 2 a. 49m 2 9n 2 c. 49m 2 42mn + 9n 2 b. 49m 2 21mn + 9n 2 d. 49m 2 + 9n Expand and simplify: (4s + 9t)(5s 4t 3) a. 20s st 12s 36t 2 27t c. 20s st + 12s 36t t b. 20s st 12s + 36t 2 27t d. 20s st 12s 36t 2 27t 42. Expand and simplify: (10v 13w)(10v + 13w) a. 100v vw + 169w 2 c. 100v 2 169w 2 b. 100v w 2 d. 100v 2 260vw + 169w Expand and simplify: (4d 1)(5d d 3) a. 20d d c. 20d d 2 24d + 3 b. 20d d 2 12d + 3 d. 20d d Expand and simplify: (f + 5g)(2f 5g + 7) a. 2f 2 + 5fg + 7f + 25g g c. 2f 2 + 5fg + 7f 25g g b. 2f 2 15fg + 7f 25g g d. 2f 2 5fg + 7f 25g g 5

6 45. Which polynomial, written in simplified form, represents the area of this rectangle? a. 8x 2 36xy 20y 2 c. 16x xy 40y 2 b. 8x xy 20y 2 d. 8x xy 20y Expand and simplify: (2x 2 + 5x 6)(5x 2 2x + 3) a. 10x x 3 34x x 18 c. 10x x 3 24x x + 18 b. 10x x 3 34x 2 3x + 18 d. 10x 4 29x 3 34x x Expand and simplify: (n 2 2n + 3)( 2n 2 + 7n + 8) a. 2n n 3 12n 2 + 5n + 24 c. 2n 4 3n n + 24 b. 2n n n + 24 d. 2n 4 3n 3 12n 2 + 5n Expand and simplify: (6p + 3)(6p 7) (7p 4)(p 2) a. 29p 2 42p 13 c. 29p 2 6p 29 b. 29p 2 6p 13 d. 29p 2 42p Expand and simplify: (6x y)(3x + 8y) (2x 3y) 2 a. 14x xy 17y 2 c. 14x xy + 1y 2 b. 14x xy + 1y 2 d. 14x xy 17y Expand and simplify: (3c + 2)(2c 7) + 3( 2c + 1)(7c 5) a. 36c 2 + 8c 29 c. 36c 2 8c 19 b. 36c c 29 d. 36c 2 8c Expand and simplify: (4a b 2)(3a 7) (3a + 4b) 2 a. 3a 2 34a 3ab + 7b b 2 c. 3a 2 22a 27ab + 7b b 2 b. 3a 2 34a 27ab + 7b b 2 d. 3a 2 34a + 21ab + 7b b 2 6

7 52. Each shape is a rectangle. Write a polynomial, in simplified form, to represent the area of the shaded region. a. 5x x + 66 c. 5x x + 30 b. 5x x + 30 d. 5x x Factor: 121a a + 25 a. (11a + 5)(11a 5) c. (11a 5) 2 b. (121a + 5)(a + 5) d. (11a + 5) Factor: 36 60r + 25r 2 a. (9 5r)(4a 5r) c. (6 + 5r) 2 b. (6 5r)(6 + 5r) d. (6 5r) Factor: 16p 2 81q 2 a. (4p 9q) 2 c. (16p 9q)(p 9q) b. (4p + 9q) 2 d. (4p + 9q)(4p 9q) 56. Find an integer to replace so that this trinomial is a perfect square. x xy + 9y 2 a. 7 c. 49 b. 14 d Find an integer to replace so that this trinomial is a perfect square. 64v 2 vw + 81w 2 a. 144 c. 72 b. 648 d Factor: 49s 2 112st + 64t 2 a. (7s 8t) 2 c. (7s t)(7s 64t) b. (7s + 8t) 2 d. (7s 8t)(7s + 8t) 59. Identify this polynomial as a perfect square trinomial, a difference of squares, or neither. 9a 2 + 9a + 36 a. Difference of squares c. Neither b. Perfect square trinomial 7

8 60. Identify this polynomial as a perfect square trinomial, a difference of squares, or neither. 25g 2 9h 2 a. Perfect square trinomial c. Neither b. Difference of squares 61. Factor: 9c 2 12c + 4 a. (3c 2) 2 c. (6c 4) 2 b. (3c 2)(3c + 2) d. (6c 4)(6c + 4) 62. Factor: 8y 2 58yz + 60z 2 a. 4(2y 3z)(y 5z) c. 2(4y 5z)(y 6z) b. 2(4y + 5z)(y 6z) d. 2(4y 5z)(y + 6z) 63. Factor: 3z 4 768z 2 a. 3z 2 (z + 16)(z 16) c. z 2 (z + 48)(z 16) b. 3z 2 (z + 16) 2 d. 3z 2 (z 16) Factor: 48b bc 3c 2 a. (2b + 3c)(24b c) c. (16b + c)(3b 3c) b. (48b 3c)(b c) d. (2b 3c)(24b + c) 65. Factor: 8m 2 34mn + 33n 2 a. (4m 11n)(2m 3n) c. (4m + 11n)(2m + 3n) b. (8m 33n)(m n) d. (4m 11n)(2m + 3n) 66. Factor: 162 2w 4 a. (9 w 2 )(18 w 2 ) c. 2(9 w 2 ) 2 b. 2(9 + w 2 )(3 + w)(3 w) d. 2(9 + w 2 ) Determine the area of the shaded region in factored form. a. 4(x + 12) c. (3x + 12)(x + 2) b. (3x + 2)(x + 12) d. (3x 2)(x 12) 8

9 68. From the list, which terms are like 7x? 7x 2, 6x, 5, 8x, 7x, 8x 2, 7 a. 7x 2, 6x, 8x, 7x, 8x 2 c. 7x b. 6x, 8x, 7x d. 7x 2, 7x, These algebra tiles may be used in the following question. x 2 x 2 x x 1 1 Which pair of tiles represents a zero pair? i) ii) iii) iv) a. i b. ii c. iii d. iv 70. Combine like terms. 6x + 5x 2 + 4x + 2x 2 a. 5x 2 b. 2x 2 + 7x 4 c. 2x + 7x 2 d. 5x 71. These algebra tiles may be used in the following question. x 2 x 2 x x 1 1 Write the polynomial sum modelled by this set of tiles. a. ( x 2 3x 4) + ( x 2 + x + 4) c. ( 2) + ( 2) + 0 b. (x 2 + 3x + 4) + (x 2 + x + 4) d Add. ( 5 6x 2 ) + (8x 2 + 7) a. 4x 2 b x 4 c. 4 d x 2 9

10 73. Add. ( 5 + 5r + 5r 2 ) + ( 2 8r 2 7r) a. 7 2r 2 3r 4 c. 7 2r 3r 2 b. 2 3r 2r 2 d. 2r 2 3r These algebra tiles may be used in the following question. x 2 x 2 x x 1 1 Write the subtraction sentence that these algebra tiles represent. a. (x 2 + 3x + 2) (x 2 + x + 2) = 2x b. ( x 2 3x + 2) ( x 2 x + 2) = 2x c. ( x 2 x + 2) ( x 2 3x + 2) = 2x d. (x 2 + x + 2) (x 2 + 3x + 2) = 2x 75. Subtract. ( 3n 2 + 8) (5 7n 2 ) a. 10n c. 10n b. 8n d. 4n Subtract. ( 4b 6b 2 2) (8b + 8 7b 2 ) a. 12b 13b 2 10 c. b 14b b. 12b 13b d. 12b + b

11 77. These algebra tiles may be used in the following question. x 2 x 2 x x 1 1 What product is modelled by this set of algebra tiles? a. 3(x 2 4x 3) c. 3(x 2 + 4x + 3) b. 3( x 2 4x + 3) d. 3(x 2 4x + 3) 78. Write the multiplication sentence modelled by this rectangle. a. 2(4x + 7) = 8x + 14 c. 2(4x) + 7 = 8x + 7 b. 2(4x 7) = 8x 14 d. 2(4x + 7) = 8x Multiply: 9(5x 2 4x) a. 45x 2 + 5x b. 45x 2 4x c. 14x 2 5x d. 45x 2 36x 80. Multiply: 4(7c 2 5c 3) a. 28c 2 5c 3 c. 28c c + 12 b. 3c 2 9c 7 d. 28c 2 20c Write the multiplication sentence modelled by this set of algebra tiles. a. 2z(4z 2 + 8z) = 2z + 4 c. z(2z + 4) = 2z 2 + 4z b. 2z(2z + 4) = 4z 2 + 8z d. 2(2z 2 + 4) = 4z

12 82. Write the multiplication sentence modelled by this rectangle. a. 2x(4x) + 5 = 8x c. 2x(4x + 5) = 8x x b. 2x(4x + 5) = 6x + 5 d. 4x(2x + 5) = 8x x 83. Multiply: 5w(7w) a. 35w 2 b. 12w 2 c. 35w 2 d. 2w Multiply: 6c(4c 5) a. 2c b. 24c c c. 24c 2 30c d. 24c How many terms are in the polynomial below? 4a 4 a. 4 b. 3 c. 2 d Is the polynomial below a monomial, binomial, or trinomial? 2p a. Monomial c. Trinomial b. Binomial d. None of the above Short Answer 87. Write an expression for the width of this rectangle. 88. Factor: s 2 33s Expand and simplify: (11t + 2)(4t 3) 90. Factor: 22n 2 + n 5 12

13 91. Factor: 14z 2 49z Expand and simplify: (9z 2 2z + 10)(3z + 12) 93. Expand and simplify: (7x 2y)(3x + 7y 9) 94. Expand and simplify: ( x 4) Expand and simplify: ( 2x + 1) Expand and simplify: 3( a + 2) Find and correct the errors in this solution. (11a + b)(2a 13b + 4) = 13a 2 143ab + 44a 2ab 13b 2 + 4b = 13a 2 145ab 13b 2 44a + 4b 98. Factor: 36a ab + 121b Factor: 49s 2 64t Factor fully: 21p 2 r 165pqr 24q 2 r 101. Find an integer to replace so that the trinomial is a perfect square. 121x 2 308xy + y 2 Problem 102. Multiply this pair of binomials. Sketch and label a rectangle to illustrate the product. ( x + 9) ( x 4) 103. Factor. Check by expanding. n 2 + n Factor. Check by expanding. 8z 2 112z

14 105. Find the area of the rectangle Write a polynomial to represent the area of this rectangle. Simplify the polynomial A student says that the expression 10r r 2 93r 90 represents the volume of this right rectangular prism. Is the student correct? How do you know? 108. Factor. Explain your steps. 196x 2 16y 2 14

15 109. A picture and its frame have dimensions as shown. a) Find an expression for the area of the frame, in factored form. b) Determine the area of the frame when s = 15 cm Identify the equivalent polynomials. Justify your answer. i) 1 + 2x x x ii) 6x 2 + 6x 3 3x + 7 4x 2 iii) 3x x x The diagram below shows one rectangle inside another. a) Determine the area of each rectangle. b) Determine the area of the shaded region. 15

16 Math 10 - Unit 5 Final Review - Polynomials Answer Section MULTIPLE CHOICE 1. C 2. D 3. B 4. C 5. D 6. B 7. A 8. B 9. C 10. A 11. A 12. C 13. C 14. D 15. B 16. D 17. D 18. B 19. C 20. B 21. B 22. A 23. A 24. D 25. B 26. B 27. A 28. B 29. C 30. B 31. A 32. D 33. A 34. B 35. C 36. D 37. C 38. C 39. C 1

17 40. C 41. A 42. C 43. C 44. C 45. D 46. A 47. A 48. C 49. D 50. B 51. B 52. A 53. D 54. D 55. D 56. C 57. A 58. A 59. C 60. B 61. A 62. C 63. A 64. A 65. A 66. B 67. B 68. B 69. B 70. C 71. A 72. D 73. C 74. B 75. D 76. D 77. D 78. A 79. D 80. C 81. B 82. C 83. A 84. B 2

18 85. C 86. A SHORT ANSWER 87. a + 6b 88. ( s 32) ( s 1) t 2 25t ( 11n 5) ( 2n + 1) 91. 7( 2z 5) ( z 1) z z 2 + 6z x xy 14y 2 63x + 18y 94. x 3 12x x x x 2 + 6x a 3 18a 2 36x (11a + b)(2a 13b + 4) = 22a 2 143ab + 44a + 2ab 13b 2 + 4b = 22a 2 141ab + 44a 13b 2 + 4b 98. ( 6a + 11b) ( 7s + 8t) ( 7s 8t) rÊ Ë Á7p + qˆ Ê Ë Á p 8qˆ PROBLEM 102. ( x + 9) ( x 4) = x 2 + ( 4x) + 9x + ( 36) = (x 2 + 5x 36) 3

19 103. Two numbers with a sum of 1 and a product of 42 are 7 and 6. So, n 2 + n 42 = (n + 7)(n 6) Check that the factors are correct. Multiply the factors. (n + 7)(n 6) = n 2 6n + 7n 42 = n 2 + n 42 This trinomial is the same as the original trinomial, so the factors are correct z 2 112z The greatest common factor is 8. 8z 2 112z = 8(z 2 14z + 45) Two numbers with a sum of 14 and a product of 45 are 5 and 9. So, z 2 14z + 45 = (z 5)(z 9) And, 8z 2 112z = 8(z 5)(z 9) Check that the factors are correct. Multiply the factors. 8(z 5)(z 9) = 8(z 2 14z + 45) = 8z 2 112z The trinomial is the same as the original trinomial, so the factors are correct Use the formula for the area, A, of a rectangle. A = l w A = ( 5b 6) ( 3b 2) Use the distributive property. A = 5b(3b 2) + ( 6)(3b 2) A = 15b 2 10b 18b + 12 A = 15b 2 28b + 12 The area of the rectangle is 15b 2 28b + 12 square units. 4

20 106. Use the formula for the area, A, of a rectangle: A = lw A = (4x 5y)(6x + 3y) A = 4x(6x) + 4x(3y) 5y(6x) 5y(3y) A = 24x xy 30xy 15y 2 A = 24x 2 18xy 15y 2 The expression 24x 2 18xy 15y 2 represents the area of this rectangle Use the formula for the volume, V, of a right rectangular prism: V = lwh x 2 16y 2 V = (5r 6)(2r + 3)(r + 5) V = (10r r 12r 18)(r + 5) V = (10r 2 + 3r 18)(r + 5) V = 10r 2 (r) + 10r 2 (5) + 3r(r) + 3r(5) 18(r) 18(5) V = 10r r 2 + 3r 90 Since this expression does not match the student s expression, the student is incorrect. The expression 10r r 2 + 3r 90 represents the volume of the right rectangular prism. As written, each term of the binomial is not a perfect square. But the terms have a common factor 4. Remove this common factor. 196x 2 16y 2 = 4(49x 2 4y 2 ) Write each term in the binomial as a perfect square. È 4(49x 2 4y 2 ) = 4 (7x) 2 (2y) 2 ÎÍ = 4(7x 2y)(7x + 2y) Write these terms in binomial factors. 5

21 109. a) The area, A, of the larger square is: ( 8s) 2 = 64s 2 The area, A, of the smaller square is: (8s 4 4) 2 = ( 8s 8) 2 The area, A, of the frame is: A = 64s 2 (64s 2 128s + 64) A = 64s 2 64s s 64 A = 128s 64 A = 64(2s 1) = 64s 2 128s + 64 b) When s = 15 cm, the area, A square centimetres, of the frame is: A = 64(2s 1) È A = 64 ÎÍ 2( 15) 1 A = 1856 The area of the frame is 1856 cm Simplify each polynomial. i) 1 + 2x x x = 2x x 11x = 2x 2 + 3x + 4 ii) 6x 2 + 6x 3 3x + 7 4x 2 = 6x 2 4x 2 + 6x 3x = 2x 2 + 3x + 4 iii) 3x x x 2 = 8x 2 6x 2 + 3x = 2x 2 + 3x + 7 Polynomials i and ii are equivalent because they both simplify to the same polynomial: 2x 2 + 3x a) The outer rectangle has dimensions 9y and 6y. Its area is: (9y)(6y) = 54y 2 The inner rectangle has dimensions 5y and 3y. Its area is: (5y)(3y) = 15y 2 b) The total area of the shaded region is the difference in the areas of the rectangles: 54y 2 15y 2 = 39y 2 6

### Unit 3 Factors & Products

1 Unit 3 Factors & Products General Outcome: Develop algebraic reasoning and number sense. Specific Outcomes: 3.1 Demonstrate an understanding of factors of whole number by determining the: o prime factors

### review To find the coefficient of all the terms in 15ab + 60bc 17ca: Coefficient of ab = 15 Coefficient of bc = 60 Coefficient of ca = -17

1. Revision Recall basic terms of algebraic expressions like Variable, Constant, Term, Coefficient, Polynomial etc. The coefficients of the terms in 4x 2 5xy + 6y 2 are Coefficient of 4x 2 is 4 Coefficient

### Algebraic Expressions

Algebraic Expressions 1. Expressions are formed from variables and constants. 2. Terms are added to form expressions. Terms themselves are formed as product of factors. 3. Expressions that contain exactly

### Unit 3: Review for Final Exam

Unit 3: Review for Final Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Write the prime factorization of 1386. a. b. c. d. 2. Determine the greatest

### Get Ready. 6. Expand using the distributive property. a) 6m(2m 4) b) 8xy(2x y) c) 6a 2 ( 3a + 4ab) d) 2a(b 2 6ab + 7)

Get Ready BLM 5 1... Classify Polynomials 1. Classify each polynomial by the number of terms. 2y x 2 + 3x + 2 c) 6x 2 y + 2xy + 4 d) x 2 + y 2 e) 3x 2 + 2x + y 4 6. Expand using the distributive property.

### Math 10-C Polynomials Concept Sheets

Math 10-C Polynomials Concept Sheets Concept 1: Polynomial Intro & Review A polynomial is a mathematical expression with one or more terms in which the exponents are whole numbers and the coefficients

### Multiplication of Polynomials

Summary 391 Chapter 5 SUMMARY Section 5.1 A polynomial in x is defined by a finite sum of terms of the form ax n, where a is a real number and n is a whole number. a is the coefficient of the term. n is

### 7-7 Multiplying Polynomials

Example 1: Multiplying Monomials A. (6y 3 )(3y 5 ) (6y 3 )(3y 5 ) (6 3)(y 3 y 5 ) 18y 8 Group factors with like bases together. B. (3mn 2 ) (9m 2 n) Example 1C: Multiplying Monomials Group factors with

### Collecting Like Terms

MPM1D Unit 2: Algebra Lesson 5 Learning goal: how to simplify algebraic expressions by collecting like terms. Date: Collecting Like Terms WARM-UP Example 1: Simplify each expression using exponent laws.

### To Find the Product of Monomials. ax m bx n abx m n. Let s look at an example in which we multiply two monomials. (3x 2 y)(2x 3 y 5 )

5.4 E x a m p l e 1 362SECTION 5.4 OBJECTIVES 1. Find the product of a monomial and a polynomial 2. Find the product of two polynomials 3. Square a polynomial 4. Find the product of two binomials that

### Mathwithsheppard.weebly.com

Unit #: Powers and Polynomials Unit Outline: Date Lesson Title Assignment Completed.1 Introduction to Algebra. Discovering the Exponent Laws Part 1. Discovering the Exponent Laws Part. Multiplying and

### Chapter y. 8. n cd (x y) 14. (2a b) 15. (a) 3(x 2y) = 3x 3(2y) = 3x 6y. 16. (a)

Chapter 6 Chapter 6 opener A. B. C. D. 6 E. 5 F. 8 G. H. I. J.. 7. 8 5. 6 6. 7. y 8. n 9. w z. 5cd.. xy z 5r s t. (x y). (a b) 5. (a) (x y) = x (y) = x 6y x 6y = x (y) = (x y) 6. (a) a (5 a+ b) = a (5

### Polynomials Practice Test

Name: Class: Date: Polynomials Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. From the list, which terms are like 7x? 7x 2, 6x, 5, 8x, 7x,

### POLYNOMIAL: A polynomial is a or the

MONOMIALS: CC Math I Standards: Unit 6 POLYNOMIALS: INTRODUCTION EXAMPLES: A number 4 y a 1 x y A variable NON-EXAMPLES: Variable as an exponent A sum x x 3 The product of variables 5a The product of numbers

### 5.1 Modelling Polynomials

5.1 Modelling Polynomials FOCUS Model, write, and classify polynomials. In arithmetic, we use Base Ten Blocks to model whole numbers. How would you model the number 234? In algebra, we use algebra tiles

### ( ) Chapter 6 ( ) ( ) ( ) ( ) Exercise Set The greatest common factor is x + 3.

Chapter 6 Exercise Set 6.1 1. A prime number is an integer greater than 1 that has exactly two factors, itself and 1. 3. To factor an expression means to write the expression as the product of factors.

### Chapter 5: Exponents and Polynomials

Chapter 5: Exponents and Polynomials 5.1 Multiplication with Exponents and Scientific Notation 5.2 Division with Exponents 5.3 Operations with Monomials 5.4 Addition and Subtraction of Polynomials 5.5

### Maintaining Mathematical Proficiency

Chapter 7 Maintaining Mathematical Proficiency Simplify the expression. 1. 5x 6 + 3x. 3t + 7 3t 4 3. 8s 4 + 4s 6 5s 4. 9m + 3 + m 3 + 5m 5. 4 3p 7 3p 4 1 z 1 + 4 6. ( ) 7. 6( x + ) 4 8. 3( h + 4) 3( h

### 5.1, 5.2, 5.3 Properites of Exponents last revised 6/7/2014. c = Properites of Exponents. *Simplify each of the following:

48 5.1, 5.2, 5.3 Properites of Exponents last revised 6/7/2014 Properites of Exponents 1. x a x b = x a+b *Simplify each of the following: a. x 4 x 8 = b. x 5 x 7 x = 2. xa xb = xa b c. 5 6 5 11 = d. x14

### MATHEMATICS 9 CHAPTER 7 MILLER HIGH SCHOOL MATHEMATICS DEPARTMENT NAME: DATE: BLOCK: TEACHER: Miller High School Mathematics Page 1

MATHEMATICS 9 CHAPTER 7 NAME: DATE: BLOCK: TEACHER: MILLER HIGH SCHOOL MATHEMATICS DEPARTMENT Miller High School Mathematics Page 1 Day 1: Creating expressions with algebra tiles 1. Determine the multiplication

### Polynomials 370 UNIT 10 WORKING WITH POLYNOMIALS. The railcars are linked together.

UNIT 10 Working with Polynomials The railcars are linked together. 370 UNIT 10 WORKING WITH POLYNOMIALS Just as a train is built from linking railcars together, a polynomial is built by bringing terms

### Unit 13: Polynomials and Exponents

Section 13.1: Polynomials Section 13.2: Operations on Polynomials Section 13.3: Properties of Exponents Section 13.4: Multiplication of Polynomials Section 13.5: Applications from Geometry Section 13.6:

Algebra I Book 2 Powered by... ALGEBRA I Units 4-7 by The Algebra I Development Team ALGEBRA I UNIT 4 POWERS AND POLYNOMIALS......... 1 4.0 Review................ 2 4.1 Properties of Exponents..........

### Review Unit Multiple Choice Identify the choice that best completes the statement or answers the question.

Review Unit 3 1201 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following numbers is not both a perfect square and a perfect cube? a. 531

### Quick-and-Easy Factoring. of lower degree; several processes are available to fi nd factors.

Lesson 11-3 Quick-and-Easy Factoring BIG IDEA Some polynomials can be factored into polynomials of lower degree; several processes are available to fi nd factors. Vocabulary factoring a polynomial factored

### = The algebraic expression is 3x 2 x The algebraic expression is x 2 + x. 3. The algebraic expression is x 2 2x.

Chapter 7 Maintaining Mathematical Proficiency (p. 335) 1. 3x 7 x = 3x x 7 = (3 )x 7 = 5x 7. 4r 6 9r 1 = 4r 9r 6 1 = (4 9)r 6 1 = 5r 5 3. 5t 3 t 4 8t = 5t t 8t 3 4 = ( 5 1 8)t 3 4 = ()t ( 1) = t 1 4. 3(s

### Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2

Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2 April 11, 2016 Chapter 10 Section 1: Addition and Subtraction of Polynomials A monomial is

Adding and Subtracting Polynomials Polynomial A monomial or sum of monomials. Binomials and Trinomial are also polynomials. Binomials are sum of two monomials Trinomials are sum of three monomials Degree

### Real Numbers. Real numbers are divided into two types, rational numbers and irrational numbers

Real Numbers Real numbers are divided into two types, rational numbers and irrational numbers I. Rational Numbers: Any number that can be expressed as the quotient of two integers. (fraction). Any number

### Beginning Algebra MAT0024C. Professor Sikora. Professor M. J. Sikora ~ Valencia Community College

Beginning Algebra Professor Sikora MAT002C POLYNOMIALS 6.1 Positive Integer Exponents x n = x x x x x [n of these x factors] base exponent Numerical: Ex: - = where as Ex: (-) = Ex: - = and Ex: (-) = Rule:

### Lesson 3: Polynomials and Exponents, Part 1

Lesson 2: Introduction to Variables Assessment Lesson 3: Polynomials and Exponents, Part 1 When working with algebraic expressions, variables raised to a power play a major role. In this lesson, we look

### 5.3. Polynomials and Polynomial Functions

5.3 Polynomials and Polynomial Functions Polynomial Vocabulary Term a number or a product of a number and variables raised to powers Coefficient numerical factor of a term Constant term which is only a

### Algebra I. Polynomials.

1 Algebra I Polynomials 2015 11 02 www.njctl.org 2 Table of Contents Definitions of Monomials, Polynomials and Degrees Adding and Subtracting Polynomials Multiplying a Polynomial by a Monomial Multiplying

### When you square a binomial, you can apply the FOIL method to find the product. You can also apply the following rules as a short cut.

Squaring a Binomial When you square a binomial, you can apply the FOIL method to find the product. You can also apply the following rules as a short cut. Solve. (x 3) 2 Step 1 Square the first term. Rules

### Algebra. Practice Pack

Algebra Practice Pack WALCH PUBLISHING Table of Contents Unit 1: Algebra Basics Practice 1 What Are Negative and Positive Numbers?... 1 Practice 2 Larger and Smaller Numbers................ 2 Practice

### CHAPTER 1 POLYNOMIALS

1 CHAPTER 1 POLYNOMIALS 1.1 Removing Nested Symbols of Grouping Simplify. 1. 4x + 3( x ) + 4( x + 1). ( ) 3x + 4 5 x 3 + x 3. 3 5( y 4) + 6 y ( y + 3) 4. 3 n ( n + 5) 4 ( n + 8) 5. ( x + 5) x + 3( x 6)

### Multiplying Monomials

320 Chapter 5 Polynomials Eample 1 Multiplying Monomials Multiply the monomials. a. 13 2 y 7 215 3 y2 b. 1 3 4 y 3 21 2 6 yz 8 2 a. 13 2 y 7 215 3 y2 13 521 2 3 21y 7 y2 15 5 y 8 Group coefficients and

### MATH98 Intermediate Algebra Practice Test Form A

MATH98 Intermediate Algebra Practice Test Form A MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) (y - 4) - (y + ) = 3y 1) A)

### Solutions Key Exponents and Polynomials

CHAPTER 7 Solutions Key Exponents and Polynomials ARE YOU READY? PAGE 57. F. B. C. D 5. E 6. 7 7. 5 8. (-0 9. x 0. k 5. 9.. - -( - 5. 5. 5 6. 7. (- 6 (-(-(-(-(-(- 8 5 5 5 5 6 8. 0.06 9.,55 0. 5.6. 6 +

### Algebra I Polynomials

Slide 1 / 217 Slide 2 / 217 Algebra I Polynomials 2014-04-24 www.njctl.org Slide 3 / 217 Table of Contents Definitions of Monomials, Polynomials and Degrees Adding and Subtracting Polynomials Multiplying

### Algebraic Expressions and Identities

9 Algebraic Epressions and Identities introduction In previous classes, you have studied the fundamental concepts of algebra, algebraic epressions and their addition and subtraction. In this chapter, we

### ( ) Chapter 7 ( ) ( ) ( ) ( ) Exercise Set The greatest common factor is x + 3.

Chapter 7 Exercise Set 7.1 1. A prime number is an integer greater than 1 that has exactly two factors, itself and 1. 3. To factor an expression means to write the expression as the product of factors.

### RAVEN S MANITOBA GRADE 10 INTRODUCTION TO APPLIED AND PRE CALCULUS MATHEMATICS (20S)

RAVEN S MANITOBA GRADE 10 INTRODUCTION TO APPLIED AND PRE CALCULUS MATHEMATICS (20S) LINKED DIRECTLY TO NEW CURRICULUM REQUIREMENTS FROM THE WESTERN PROTOCOLS FOR 2008 AND BEYOND STUDENT GUIDE AND RESOURCE

### Chapter Six. Polynomials. Properties of Exponents Algebraic Expressions Addition, Subtraction, and Multiplication Factoring Solving by Factoring

Chapter Six Polynomials Properties of Exponents Algebraic Expressions Addition, Subtraction, and Multiplication Factoring Solving by Factoring Properties of Exponents The properties below form the basis

### Chapter 8 Polynomials and Factoring

Chapter 8 Polynomials and Factoring 8.1 Add and Subtract Polynomials Monomial A. EX: Degree of a monomial the of all of the of the EX: 4x 2 y Polynomial A or EX: Degree of a polynomial the of its terms

### Chapter 3: Section 3.1: Factors & Multiples of Whole Numbers

Chapter 3: Section 3.1: Factors & Multiples of Whole Numbers Prime Factor: a prime number that is a factor of a number. The first 15 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,

### Why It s Important. What You ll Learn

How could you solve this problem? Denali and Mahala weed the borders on the north and south sides of their rectangular yard. Denali starts first and has weeded m on the south side when Mahala says he should

### Intensive Math-Algebra I Mini-Lesson MA.912.A.4.3

Intensive Math-Algebra I Mini-Lesson M912.4.3 Summer 2013 Factoring Polynomials Student Packet Day 15 Name: Date: Benchmark M912.4.3 Factor polynomials expressions This benchmark will be assessed using

### Algebra 1: Hutschenreuter Chapter 10 Notes Adding and Subtracting Polynomials

Algebra 1: Hutschenreuter Chapter 10 Notes Name 10.1 Adding and Subtracting Polynomials Polynomial- an expression where terms are being either added and/or subtracted together Ex: 6x 4 + 3x 3 + 5x 2 +

### Algebraic Expressions and Identities

ALGEBRAIC EXPRESSIONS AND IDENTITIES 137 Algebraic Expressions and Identities CHAPTER 9 9.1 What are Expressions? In earlier classes, we have already become familiar with what algebraic expressions (or

### 8 th Grade Honors Variable Manipulation Part 3 Student

8 th Grade Honors Variable Manipulation Part 3 Student 1 MULTIPLYING BINOMIALS-FOIL To multiply binomials, use FOIL: First, Outer, Inner, Last: Example: (x + 3)(x + 4) First multiply the First terms: x

### Chapter 7: Exponents

Chapter : Exponents Algebra Chapter Notes Name: Notes #: Sections.. Section.: Review Simplify; leave all answers in positive exponents:.) m -.) y -.) m 0.) -.) -.) - -.) (m ) 0.) 0 x y Evaluate if a =

### MATH98 Intermediate Algebra Practice Test Form B

MATH98 Intermediate Algebra Practice Test Form B MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) (y - 4) - (y + 9) = y 1) -

### Something that can have different values at different times. A variable is usually represented by a letter in algebraic expressions.

Lesson Objectives: Students will be able to define, recognize and use the following terms in the context of polynomials: o Constant o Variable o Monomial o Binomial o Trinomial o Polynomial o Numerical

### SECTION 1.4 PolyNomiAls feet. Figure 1. A = s 2 = (2x) 2 = 4x 2 A = 2 (2x) 3 _ 2 = 1 _ = 3 _. A = lw = x 1. = x

SECTION 1.4 PolyNomiAls 4 1 learning ObjeCTIveS In this section, you will: Identify the degree and leading coefficient of polynomials. Add and subtract polynomials. Multiply polynomials. Use FOIL to multiply

### F.3 Special Factoring and a General Strategy of Factoring

F.3 Special Factoring and a General Strategy of Factoring Difference of Squares section F4 233 Recall that in Section P2, we considered formulas that provide a shortcut for finding special products, such

### Find two positive factors of 24 whose sum is 10. Make an organized list.

9.5 Study Guide For use with pages 582 589 GOAL Factor trinomials of the form x 2 1 bx 1 c. EXAMPLE 1 Factor when b and c are positive Factor x 2 1 10x 1 24. Find two positive factors of 24 whose sum is

### 1 of 32 4/24/2018, 11:38 AM

1 of 3 4/4/018, 11:38 AM Student: Date: Instructor: Alfredo Alvarez Course: Math 0410 Spring 018 Assignment: Math 0410 Homework149aleks 1 Insert < or > between the pair of integers to make the statement

### LESSON 7.2 FACTORING POLYNOMIALS II

LESSON 7.2 FACTORING POLYNOMIALS II LESSON 7.2 FACTORING POLYNOMIALS II 305 OVERVIEW Here s what you ll learn in this lesson: Trinomials I a. Factoring trinomials of the form x 2 + bx + c; x 2 + bxy +

### Activity 1 Multiply Binomials. Activity 2 Multiply Binomials. You can use algebra tiles to find the product of two binomials.

Algebra Lab Multiplying Polynomials You can use algebra tiles to find the product of two binomials. Virginia SOL A..b The student will perform operations on polynomials, including adding, subtracting,

### Westside. Algebra 2 PreAP

Westside Algebra 2 PreAP Name Period IMPORTANT INSTRUCTIONS FOR STUDENTS!!! We understand that students come to Algebra II with different strengths and needs. For this reason, students have options for

### Name Period Date. Use mathematical reasoning to create polynomial expressions that generalize patterns. Practice polynomial arithmetic.

Name Period Date POLYNOMIALS Student Packet 4: Polynomial Arithmetic Applications POLY4.1 Hundred Chart Patterns Gather empirical data to form conjectures about number patterns. Write algebraic expressions.

### Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term")... so it says "many terms

Polynomials Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term")... so it says "many terms Polynomials A polynomial looks like this: Term A number, a variable, or the

### Fair Game Review. Chapter 7. Simplify the expression. Write an expression for the perimeter of the figure

Name Date Chapter 7 Simplify the expression. Fair Game Review 1. 5y + 6 9y. h + 11 + 3h 4 + + 4. 7 ( m + 8) 3. 8a 10 4a 6 a 5. 5 ( d + 3) + 4( d 6) 6. q ( q ) 16 + 9 + 7 Write an expression for the perimeter

### Review for Mastery. Integer Exponents. Zero Exponents Negative Exponents Negative Exponents in the Denominator. Definition.

LESSON 6- Review for Mastery Integer Exponents Remember that means 8. The base is, the exponent is positive. Exponents can also be 0 or negative. Zero Exponents Negative Exponents Negative Exponents in

### Westside Algebra 2 PreAP

Westside Algebra 2 PreAP Name Period IMPORTANT INSTRUCTIONS FOR STUDENTS!!! We understand that students come to Algebra II with different strengths and needs. For this reason, students have options for

### AFM Review Test Review

Name: Class: Date: AFM Review Test Review Multiple Choice Identify the choice that best completes the statement or answers the question. What are the solutions of the inequality?. q + (q ) > 0 q < 3 q

### Classifying Polynomials. Simplifying Polynomials

1 Classifying Polynomials A polynomial is an algebraic expression with one or more unlike terms linked together by + or **Polynomials can be classified by the number of terms they have: A monomial has

### Exponents and Polynomials. (5) Page 459 #15 43 Second Column; Page 466 #6 30 Fourth Column

Algebra Name: Date: Period: # Exponents and Polynomials (1) Page 453 #22 59 Left (2) Page 453 #25 62 Right (3) Page 459 #5 29 Odd (4) Page 459 #14 42 First Column; Page 466 #3 27 First Column (5) Page

### Polynomial Functions

Polynomial Functions NOTE: Some problems in this file are used with permission from the engageny.org website of the New York State Department of Education. Various files. Internet. Available from https://www.engageny.org/ccss-library.

### Lesson 6. Diana Pell. Monday, March 17. Section 4.1: Solve Linear Inequalities Using Properties of Inequality

Lesson 6 Diana Pell Monday, March 17 Section 4.1: Solve Linear Inequalities Using Properties of Inequality Example 1. Solve each inequality. Graph the solution set and write it using interval notation.

### Sections 7.2, 7.3, 4.1

Sections 7., 7.3, 4.1 Section 7. Multiplying, Dividing and Simplifying Radicals This section will discuss the rules for multiplying, dividing and simplifying radicals. Product Rule for multiplying radicals

### Math 2 Variable Manipulation Part 3 Polynomials A

Math 2 Variable Manipulation Part 3 Polynomials A 1 MATH 1 REVIEW: VOCABULARY Constant: A term that does not have a variable is called a constant. Example: the number 5 is a constant because it does not

### Summer Prep Packet for students entering Algebra 2

Summer Prep Packet for students entering Algebra The following skills and concepts included in this packet are vital for your success in Algebra. The Mt. Hebron Math Department encourages all students

### Algebra 1. Math Review Packet. Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals

Algebra 1 Math Review Packet Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals 2017 Math in the Middle 1. Clear parentheses using the distributive

### Combining Like Terms in Polynomials

Section 1 6: Combining Like Terms in Polynomials Polynomials A polynomial is an expression that has two or more terms each separated by a + or sign. If the expression has only one term it is called a monomial.

### Rising 8th Grade Math. Algebra 1 Summer Review Packet

Rising 8th Grade Math Algebra 1 Summer Review Packet 1. Clear parentheses using the distributive property. 2. Combine like terms within each side of the equal sign. Solving Multi-Step Equations 3. Add/subtract

### MAFS Algebra 1. Polynomials. Day 15 - Student Packet

MAFS Algebra 1 Polynomials Day 15 - Student Packet Day 15: Polynomials MAFS.91.A-SSE.1., MAFS.91.A-SSE..3a,b, MAFS.91.A-APR..3, MAFS.91.F-IF.3.7c I CAN rewrite algebraic expressions in different equivalent

### How could you express algebraically, the total amount of money he earned for the three days?

UNIT 4 POLYNOMIALS Math 11 Unit 4 Introduction p. 1 of 1 A. Algebraic Skills Unit 4 Polynomials Introduction Problem: Derrek has a part time job changing tires. He gets paid the same amount for each tire

### For Your Notebook E XAMPLE 1. Factor when b and c are positive KEY CONCEPT. CHECK (x 1 9)(x 1 2) 5 x 2 1 2x 1 9x Factoring x 2 1 bx 1 c

9.5 Factor x2 1 bx 1 c Before You factored out the greatest common monomial factor. Now You will factor trinomials of the form x 2 1 bx 1 c. Why So you can find the dimensions of figures, as in Ex. 61.

### Properties of Real Numbers

Pre-Algebra Properties of Real Numbers Identity Properties Addition: Multiplication: Commutative Properties Addition: Multiplication: Associative Properties Inverse Properties Distributive Properties Properties

### Factoring Polynomials. Review and extend factoring skills. LEARN ABOUT the Math. Mai claims that, for any natural number n, the function

Factoring Polynomials GOAL Review and extend factoring skills. LEARN ABOUT the Math Mai claims that, for any natural number n, the function f (n) 5 n 3 1 3n 2 1 2n 1 6 always generates values that are

### Topic 7: Polynomials. Introduction to Polynomials. Table of Contents. Vocab. Degree of a Polynomial. Vocab. A. 11x 7 + 3x 3

Topic 7: Polynomials Table of Contents 1. Introduction to Polynomials. Adding & Subtracting Polynomials 3. Multiplying Polynomials 4. Special Products of Binomials 5. Factoring Polynomials 6. Factoring

### Polynomials and Factoring

7.6 Polynomials and Factoring Basic Terminology A term, or monomial, is defined to be a number, a variable, or a product of numbers and variables. A polynomial is a term or a finite sum or difference of

ID : ae-8-factorisation [1] Grade 8 Factorisation For more such worksheets visit www.edugain.com Answer the questions (1) Find factors of following polynomial A) y 2-2xy + 3y - 6x B) 3y 2-12xy - 2y + 8x

### mn 3 17x 2 81y 4 z Polynomials 32,457 Polynomials Part 1 Algebra (MS) Definitions of Monomials, Polynomials and Degrees Table of Contents

Table of ontents Polynomials efinitions of Monomials, Polynomials and egrees dding and Subtracting Polynomials Multiplying Monomials ividing by Monomials Mulitplying a Polynomial by a Monomial Multiplying

### Name: Chapter 7: Exponents and Polynomials

Name: Chapter 7: Exponents and Polynomials 7-1: Integer Exponents Objectives: Evaluate expressions containing zero and integer exponents. Simplify expressions containing zero and integer exponents. You

### Polynomials. In many problems, it is useful to write polynomials as products. For example, when solving equations: Example:

Polynomials Monomials: 10, 5x, 3x 2, x 3, 4x 2 y 6, or 5xyz 2. A monomial is a product of quantities some of which are unknown. Polynomials: 10 + 5x 3x 2 + x 3, or 4x 2 y 6 + 5xyz 2. A polynomial is a

### The number part of a term with a variable part. Terms that have the same variable parts. Constant terms are also like terms.

Algebra Notes Section 9.1: Add and Subtract Polynomials Objective(s): To be able to add and subtract polynomials. Recall: Coefficient (p. 97): Term of a polynomial (p. 97): Like Terms (p. 97): The number

### Controlling the Population

Lesson.1 Skills Practice Name Date Controlling the Population Adding and Subtracting Polynomials Vocabulary Match each definition with its corresponding term. 1. polynomial a. a polynomial with only 1

### Unit # 4 : Polynomials

Name: Block: Teacher: Miss Zukowski Date Submitted: / / 2018 Unit # 4 : Polynomials Submission Checklist: (make sure you have included all components for full marks) Cover page & Assignment Log Class Notes

### 27 Wyner Math 2 Spring 2019

27 Wyner Math 2 Spring 2019 CHAPTER SIX: POLYNOMIALS Review January 25 Test February 8 Thorough understanding and fluency of the concepts and methods in this chapter is a cornerstone to success in the

### I CAN classify polynomials by degree and by the number of terms.

13-1 Polynomials I CAN classify polynomials by degree and by the number of terms. 13-1 Polynomials Insert Lesson Title Here Vocabulary monomial polynomial binomial trinomial degree of a polynomial 13-1

### Algebra I Lesson 6 Monomials and Polynomials (Grades 9-12) Instruction 6-1 Multiplying Polynomials

In algebra, we deal with different types of expressions. Grouping them helps us to learn rules and concepts easily. One group of expressions is called polynomials. In a polynomial, the powers are whole

Unit 5 Quadratic Expressions and Equations 1/9/2017 2/8/2017 Name: By the end of this unit, you will be able to Add, subtract, and multiply polynomials Solve equations involving the products of monomials

### ACTIVITY: Factoring Special Products. Work with a partner. Six different algebra tiles are shown below.

7.9 Factoring Special Products special products? How can you recognize and factor 1 ACTIVITY: Factoring Special Products Work with a partner. Six different algebra tiles are shown below. 1 1 x x x 2 x