( 4 p 3. ( 2 p 2. ( x 3 y 4. ( y. (2 p 2 ) 2 ( q 4 ) 2. ( x 2 ) POLYNOMIALS, PAGES CHECK IT OUT! PAGES
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1 8. _ x 4 y 8 x 4-6 y 8-6 x 6 y 6 x - y y x 9. 5 m n 4 5 m - n 4-1 m n 5 m 0 n ( 3 5) _ ( 4 p n 3 5 n _ ) p q ( 4 p 3-1 q -4 ) ( p q -4 ) ( p q 4 ) ( p ) ( q 4 ) _ ( p ) q 8 4 p 4 q 8 3. ( 5 6) - ( 6 5) _ 33. ( x 3 y 4 x y 5 ) ( x 3-1 y 4-5 ) -3 ( x y -1 ) -3 ( x -3 y ) ( y x ) 3 y 3 ( x ) 3 y 3 x ( ) ( 10 6) _ ( ) ( ) ( ) ( ) _ POLYNOMIALS, PAGES CHECK IT OUT! PAGES a. The degree is 3. b. The degree is 1. c. The degree is 3. a. 5x: degree 1-6: degree 0 b. x 3 y : degree 5 x y 3 : degree 5 - x 4 : degree 4 : degree 0 The degree of the polynomial is 5. 3a x + x x 3 x x 3-4 x + 16 b. 18 y 5-3 y y -3 y y y The leading coefficient is -3. 4a. Degree: 3 Terms: 4 x 3 + x -x + is a cubic polynomial. b. Degree: 0 Terms: 1 6 is a constant monomial. c. Degree: 8 Terms: 3-3 y y y is an 8th-degree trinomial t + 400t (5) + 400(5) (5) + 400(5) When the firework explodes, it will be 1606 ft above the ground. THINK AND DISCUSS, PAGE Possible answer: x + 3 x -3 contains an expression with a negative exponent. 1 - a contains a variable within a denominator. b Copyright by Holt, Rinehart and Winston. 65 Holt Algebra 1
2 . 3. Degree: 4 Terms: 4 q q q 4 is a quartic polynomial. 4. Degree: 3 Terms: 5 k + 7 k 3 is a cubic binomial. 5. Degree: 4 Terms: 3 a a - a 4 is a quartic trinomial. EXERCISES, PAGES GUIDED PRACTICE, PAGE d. c 3. a 4. The degree is The degree is The degree is The degree is x : degree -x: degree 1 1: degree 0 The degree of the polynomial is a b: degree 3 a 3 b 5 : degree 8 The degree of the polynomial is y: degree 1-84 y 3 : degree 3 100: degree 0-3 y : degree 11. r 3 : degree 3 r : degree -5: degree 0 1. a 3 : degree 3 a : degree -a: degree k 4 : degree 4 k 3 : degree 3 - k : degree k: degree 1 The degree of the polynomial is b b b - b a 8-8 a 9-8 a a 8 The leading coefficient is s - 3s s 7 - s s - 3s x + 3 x x + x - 1 The leading coefficient is g g g + 5g c + 5 c c c c c - 4 The leading coefficient is Degree: Terms: 3 x + x + 3 is a quadratic trinomial. 1. Degree: 1 Terms: x - 7 is a linear binomial.. Degree: 4 Terms: k + 5 k 4 is a quartic trinomial r rl 3.14 (6) (6)(10) 3.14(36) (6)(10) The surface area of the cone is approximately cm. PRACTICE AND PROBLEM SOLVING, PAGES The degree is The degree is The degree is The degree is The degree is The degree is The degree is The degree is a : degree a 4 : degree 4-6a: degree 1 The degree of the polynomial is b: degree 1-5: degree y : degree -4.1y: degree 1-6: degree 0 The degree of the polynomial is f 4 : degree 4 f 6 : degree 6 10 f 8 : degree 8 The degree of the polynomial is n 3 : degree 3 -n: degree r 3 : degree 3 4 r 6 : degree 6 The degree of the polynomial is t 3-4 t + t 4.9 t 3-4 t + t +.5 The leading coefficient is a - 10 a a + 8a + The leading coefficient is x 7 - x + x 3 - x 5 + x 10 x 10 + x 7 - x 5 + x 3 - x 44. -m m -3 m - m + 7 The leading coefficient is x + 5x x 3 5 x x + 5x - 4 The leading coefficient is n n - n - n d + 3 d - d d d + 4d s + 1 s s s + 6 Copyright by Holt, Rinehart and Winston. 66 Holt Algebra 1
3 49. 4 x - x 5 - x x 5 - x x Degree: 0 Terms: 1 1 is a constant monomial. 51. Degree: 1 Terms: 1 6k is a linear monomial. 5. Degree: 3 Terms: x 3-4.1x - 6 is a cubic trinomial. 53. Degree: Terms: 3 4g + g - 3 is a quadratic trinomial. 54. Degree: Terms: x - 6x is a quadratic binomial. 55. Degree: 4 Terms: s 3-3 s 4 is a quartic trinomial. 56. Degree: 3 Terms: 3 c c 3 is a cubic trinomial. 57. Degree: Terms: 1 - y is a quadratic monomial v v 3.675(30) (30) 3.675(30) (900) The stopping distance of a car traveling at 30 mi/h is ft. 59. always 60. sometimes 61. never 6. sometimes 63a. 4 c 3-39 c c 4 (1) 3-39 (1) (1) 4(1) - 39(1) (1) The volume of the box when c 1 in. is 58.5 in 3. b. 4 c 3-39 c c 4 (1.5) 3-39 (1.5) (1.5) 4(3.375) - 39(.5) (1.5) The volume of the box when c 1.5 in. is 66 in 3. c. 4 c 3-39 c c 4 (4.5) 3-39 (4.5) (4.5) 4(76.765) - 39(18.063) (4.5) The volume of the box when c 4.5 in. is 0 in 3. d. Yes; the width of the cardboard is 8.5 in., so 4.5 in. cuts will meet, leaving nothing to fold up. Polynomial x - x 0 x x x 5 + x 3 + 4x x Possible answer: x + 3x Possible answer: 5x Possible answer: Possible answer: 6 x Possible answer: x Possible answer: x 1 - x Possible answer: First identify the degree of each term. From left to right, the degrees are 3, 0,, 4, and 1. Arrange the terms in order of decreasing degree, and move the plus or minus sign in front of each term with it: - x x x - x a. 1x: degree 1 6: degree 0 74b. 8 x : degree 1x: degree 1 The degree of the polynomial is. 75. A is incorrect. The student incorrectly multiplied -3 by - before evaluating the power. TEST PREP, PAGE C; A has degree 8, B has degree 1, C has degree 10, and D has degree. So C has the greatest degree. 77. J -3 x x - 5x (-1) (-1) - 5(-1) + 7-3(-1) + 4(1) - 5(-1) Time (s) Height (ft) The rocket will be the highest after s. CHALLENGE AND EXTEND, PAGE a m m m () () () (8) (4) () m m m (5) (5) (5) (15) (5) (5) The average length of a two-month-old baby boy is 58 cm and the average length of a five-month-old baby boy is 65 cm. b m m m (0) (0) (0) (0) (0) (0) The average length of a newborn baby boy is cm. Copyright by Holt, Rinehart and Winston. 67 Holt Algebra 1
4 c. The first three terms of the polynomial will equal 0, so just look at the constant. 80a. 4 x 5 + x b. yes; 0 < x < 1; raising a number between 0 and 1 to a higher power results in a lesser number. So if x is between 0 and 1, the bionomial with the least degree will have the greatest value. SPIRAL REVIEW, PAGE m p 83. y -4x + 5 y -4x + 5 4x + y y -4x + This system is inconsistent. It has no solution. 84. x + 8y 10 y x y -x + 5 y x This system is consistent and dependent. It has infinitely many solutions. 85. This system is consistent and independent. It has one solution , or _ ( v 4 5) ( v 4-1 w -5) v w ( v 3 w -5) ( v 3 ) w 5 ( v 3 ) ( w 5 ) ( v 3 ) 4 v 6 w 10 _ w ( p -4 ( p p ) 1-3 ) -4 3 ( p - ) -4 ( p ) -4 ( p 4 ) ( p ) 4 4 p _ x 6 y 4 x 6-4 y 4-9 x 4 y 9 x y -5 x y 5 ALGEBRA LAB: MODEL POLYNOMIAL ADDITION AND SUBTRACTION, PAGES TRY THIS, PAGES x x + x x x Copyright by Holt, Rinehart and Winston. 68 Holt Algebra 1
5 5. -3 x + 5x 9. 3x 6. x + 5x x x + x 7. 3 x + 4x 1. x - 6x x - 4x when you have enough tiles to actually remove them to model the subtraction 7-6 ADDING AND SUBTRACTING POLYNOMIALS, PAGES CHECK IT OUT! PAGES a. s + 3 s + s 5 s + s b. 4 z z z z z 4-6 c. x y 8 - x 8 - y 8 x 8 - x y 8 - y 8 x y 8 d. 9 b 3 c + 5 b 3 c - 13 b 3 c b 3 c Copyright by Holt, Rinehart and Winston. 69 Holt Algebra 1
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