CHAPTER 1 POLYNOMIALS
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1 1 CHAPTER 1 POLYNOMIALS 1.1 Removing Nested Symbols of Grouping Simplify. 1. 4x + 3( x ) + 4( x + 1). ( ) 3x x 3 + x ( y 4) + 6 y ( y + 3) 4. 3 n ( n + 5) 4 ( n + 8) 5. ( x + 5) x + 3( x 6) 6. 6( y 3) y ( y 1) 1.1 Removing Nested Symbols of Grouping
2 ( 4 x) 6x 8. ( n ) n 9. 8n 3 n ( n + 4) ( x + 5) x ( 3x 3) 11. ( x 5y ) + 3 4x 5( x + y 1) 1. ( 6) ( n m) m ( n 1) 1.1 Removing Nested Symbols of Grouping
3 ( a b) + 3 ( a + b) 14. ( 9x 6y ) x ( y 3) 15. 8n ( n) ( m + n) + ( n m) 16. ( x) ( 3y x ) ( 3 y ) a ( 5b) 3a 18. ( ) 5a a 1 3b 1 b + 4a 1.1 Removing Nested Symbols of Grouping
4 4 19. ( ) x x 4 x x + 5x 0. y y ( y y ) ab 3 ( ab + a) + 1 ( ba a). 7 9 xy ( x y ) + 8 x ( x + xy ) { } { } 3. 15x x + ( 3x + 5) ( y + 1 ) ( y 3 ) 1.1 Removing Nested Symbols of Grouping
5 5 { x } x ( x x ) ( ) { } 6. a 3 ( a 3 a + a) + ( a a ) x x 3 x y + y 1 y y { } a a 0.01( 90a 100) x ( 0.1 x 5 ) x + 3 ( x + 1 ) 1.1 Removing Nested Symbols of Grouping
6 6 1. Applying Integer Exponent Rules Simplify x x x x 4. y y y y ( n ) ( m ) 5 7. ( 3x ) 3 8. ( y ) ( 5a ) 10. ( 3b ) ( 4x y ) ( 3n m ) ( 4x)( x ) ( y ) ( 3y ) ( 3a )( a ) ( a ) 16. ( n ) ( n 3 ) ( n 4 ) a a a a ( ) 3 3x x x x ( ) ( x x y y ) ( x xyy ) ( 3n n ) ( n n n) 1. Applying Integer Exponent Rules
7 7 1. x x y y a a c c a b 8. 3 a b 9. x 3y a 4b 31. 3c a b xy 3 5z m nw 3 w x a bc 0 5 3a b c x y 1 x y 36. 3a b c 3 ab c Applying Integer Exponent Rules
8 8 37. x y z 3x y z ab c d 1 a b c ( 5x ) ( 5x ) 1 0 ( 5x ) ( 5 x ) ( a b ) ( 3 a b) 3 3a( ab ) a a a ( 3a) ( a ) a ( 4a) a 4. ( 3 ) ( 3 ) ( 1 ) 1 x y xy x y 1. Applying Integer Exponent Rules
9 ( ) + ( 10 ) ( ) ( ) x x y xy x y xy xy a a + ( a ) 1 1 ( ) ( ) 3 a a a 45. ( ) x y x y + 6x y 5 ( ) + ( ) 1 0 x y xy xy xy ( ab ) a b 9a b ( ) + ( ) ( ) a b 3 a b a b 1. Applying Integer Exponent Rules
10 Integer Exponents and Scientific Notation Use scientific notation to calculate the following. Write your answer in both scientific notation and standard notation. 1., , ,000,000 1,000, ,000,000 00,000, ( 3,000 )( 4,000,000 )( ) 8. ( )( 10,000,000 )( 4,000 ) 9. ( 0,000,000 )( 4,000,000 )( ) 10. ( )( 0.000)( 3,000 ) ,000,000 3, ,000,000,000 6,000, Integer Exponents and Scientific Notation
11 ,000 4,000, ,000 90,000, ( 1,000) ( ) ( 1,000,000 ) 18. ( )( 80,000,000 ) ( 40,000 ) 19. ( 50,000,000 )(,000,000 ) ( 5,000) 0. ( 0.006) ( 0.003) ( ) 1.3 Integer Exponents and Scientific Notation
12 1 1. ( ) ( 0.00) 3 ( 0.00) 3 4. (,000) (,000,000 ) ( 0.00) ( 00,000) ( ) 4 ( 3,000) ( )( 0.03) (,000,000 ) 4. 3 ( 0.000) ( ) Integer Exponents and Scientific Notation
13 Adding or Subtracting Polynomials Perform the indicated addition and/or subtraction. 1. ( 9x + 6x + 13) + ( 1x 8x 19). ( 3x + 9x 1) + ( 5x 11x + 4) 3. ( x + 4x 6) ( x 5x + 7) 4. ( 6x 14x 5) ( x + x 30) 5. ( x 3 y 4x y 4 8xy + 1) + ( x 3 y + 3x y 4 xy 1) 6. ( 3x 4 y 3 x 3 y + x y 9) + ( 4x 4 y 3 + 3x 3 y x y + 4xy ) 1.4 Adding or Subtracting Polynomials
14 14 7. ( 7a 9ab + 5b + 16) ( 3a 6ab 8b + 3) 8. ( 5a 3 + 4a b 7ab + b 3 17) ( a 3 6a b + 9ab + b 3 3a b ) 9. ( m + 5n) + ( m + 4n 6) ( 3n m + 7mn 1) 10. ( 15m mn + n ) ( 7m + 5nm n 9) ( 3n 8mn m + 6) 1.4 Adding or Subtracting Polynomials
15 Subtract 1p 11q + 6w 15 from the sum of 9p + 4q 8w + 18 and 8p 9q 1w Subtract 6a ab + 9a b b + a from the sum of a + 3a b 4b 3ab 5a a 4ab 3a b b a and 13. Add x + 5y 4z to the difference of 6x + 11y 16z and 10x 15y z. 14. Add 1m 4mn + 6n to the difference of m + mn 3n and 6m 8mn n. 1.4 Adding or Subtracting Polynomials
16 16 Write the polynomial expression for the unknown quantity. 15. Find the perimeter of a square whose side is given by x + x Find the perimeter of a rectangle whose length and width are given by a 7 and respectively. a + a 3, 17. Find the perimeter of a triangle whose sides are given by m + n 3, m 8n + 7, and m 6n Adding or Subtracting Polynomials
17 Find the length of a rectangle whose perimeter is given by given by 3 y y y y 4y and whose width is 19. Find the width of a rectangle if its length is given by 4a b + 8ab a b ab 6 + and its perimeter is 0. Find the third side of a triangle if the other two sides are given by 3 3 x x + 4 and its perimeter is given by 5x + x x x x x and 1.4 Adding or Subtracting Polynomials
18 Multiplying Polynomials Use special products for binomials to multiply the following. ax 3by 5ax 4by 6nx 5y nx + 7y 1. ( )( ). ( )( ) 3. ( 3a + 4b) 4. ( 6x y ) a b 3 6. x y ( 4x y 3z) 8. ( 5ab + c ) 1.5 Multiplying Polynomials
19 19 9. ( 0.1x + 0.3y ) 10. ( 1.1a 0.9b) 11. ( 9a 4b)( 9a + 4b) 1. ( 8x + 7y )( 8x 7y ) 13. ( 5a 8b 3 )( 5a + 8b 3 ) 14. ( 6n + 11n 4 )( 6n 11n 4 ) 15. x y x y a b a + b Multiplying Polynomials
20 0 17. ( 0.6n 0.7m)( 0.6n + 0.7m) 18. ( 0.01x + 0.1y )( 0.01x 0.1y ) x y x + y a b + 3c a b 3c x + ( y + 1) 3x + ( y ). ( ) ( ) 3x + 4y x 3 5y 3. ( a + 3) + ( b c ) ( a 1) ( b + 3c ) 4. ( x 1) + 3( y ) 3( x + ) + ( y + 1) 1.5 Multiplying Polynomials
21 1 5. 3a + ( b c) 6. ( ) 4x + y 5 7. ( x + y ) + ( z + 4) 8. ( m ) + ( n 3z ) 9. 3( a ) 4( b + 1) ( x + 3 ) ( y 4 ) 31. 3b ( 4a + 7) 3b + ( 4a + 7) 3. ( 5 ) ( 5 ) m n m + n 1.5 Multiplying Polynomials
22 33. ( x + 3y ) ( 4n + z) ( x + 3y ) + ( 4n + z) 34. ( a 3b) + ( x + y ) ( a 3b) ( x + y ) 35. 4( x 1) 5( y + ) 4( x 1) + 5( y + ) 36. 5( n m) ( y z) 5( n m) + ( y z) 37. ( 3n 4m + 6)( 3n 4m 8) 38. ( x 5y + )( 3x + 5y ) 39. ( 4a b + c + d ) 40. ( 3x y n 4)( 3x y + n + 4) 1.5 Multiplying Polynomials
23 3 1.6 Expanding Binomials Draw Pascal s Triangle. Expand the following using Pascal s Triangle. 1. ( x + 1) 3. ( y 1) 3 3. ( a + ) 4 4. ( b ) 4 5. ( x ) 5 6. ( y + ) Expanding Binomials
24 4 7. ( n 3) 6 8. ( m + 3) 6 9. ( + x) ( a) 7 x + y 11. ( ) 3 a b 1. ( ) 3 3a b 13. ( ) 4 x + 3y 14. ( ) Expanding Binomials
25 5 a + 3b 15. ( ) 6 3a b 16. ( ) x y a + b Expanding Binomials
26 6 0.1a + 0.b 19. ( ) 4 0.x 0.1y 0. ( ) 4 Write the Binomial Formula. Expand # 1 0 using the Binomial Formula. 1. ( x + 1) 3. ( y 1) 3 3. ( a + ) Expanding Binomials
27 7 4. ( b ) 4 5. ( x ) 5 6. ( y + ) 5 7. ( n 3) 6 8. ( m + 3) 6 9. ( + x) ( a) 7 x + y 31. ( ) 3 a b 3. ( ) Expanding Binomials
28 8 3a b 33. ( ) 4 x + 3y 34. ( ) 4 a + 3b 35. ( ) 6 3a b 36. ( ) Expanding Binomials
29 x y a + b a + 0.b 39. ( ) 4 0.x 0.1y 40. ( ) Expanding Binomials
30 Dividing Polynomials Divide. 1. ( x 3 x + ) ( x 1). ( y 3 + y + 4) ( y + 1) 3. ( y 4 + y + 4) ( y + ) 4. ( x 4 3x 1) ( x ) 1.7 Dividing Polynomials
31 31 5. ( x 4 x 1) ( x + x + 1) 6. ( y 4 + y 3 ) ( y y 1) 7. ( n 5 + n 3 n 1) ( n + n + ) 8. ( m 5 m + m 3) ( m 4) 1.7 Dividing Polynomials
32 ( x + 9) ( x + 1) 10. ( y 4) ( y 3) 11. ( x x + x 3 + ) ( 3 + x) 1. ( 6 n + n 4 + n) ( n 1+ n ) 1.7 Dividing Polynomials
33 ( y + y y 4 ) ( y + y 3 ) 14. ( m + 3m 4 + 6m 3 ) ( m + 1 m) ( 1+ x ) ( x + 1) 16. ( y 3) ( y ) 1.7 Dividing Polynomials
34 ( a + 8) ( + a) 18. ( y 16) ( y ) 19. ( n 4 + n 4 ) ( + n) 0. ( x 3 + x 4 ) ( 3 + x) 1.7 Dividing Polynomials
35 35 1. ( x + x x 3 + x 4 1) ( x 1). ( n + n 3 + 4n + 3n 4 4) ( + n ) 3. ( x + 7xy + 4y ) ( x + 4y ) 4. ( 6y + xy 15x ) ( 3x + y ) 1.7 Dividing Polynomials
36 36 5. ( x 3 + x y 3xy + y 3 ) ( x y ) 6. ( 3a 3 a b + ab + b 3 ) ( 3a + b) 1.7 Dividing Polynomials
37 37 7. ( a 4 + b 4 ) ( a + b) 8. ( y 4 x 4 ) ( y x) 1.7 Dividing Polynomials
38 38 9. ( x 5 3y 5 ) ( x y ) 30. ( 64a 6 b 6 ) ( a b) 1.7 Dividing Polynomials
39 Chapter Review Simplify. { } x + 3( x 1) ( x + 5) { }. 6 ( x y 3) + 5 x 5y 3( x y ) ( x + y ) 1.8 Chapter Review
40 40 Simplify. Your answer should contain no zero or negative exponents. 3. x y z 3xy z a b c 4. 3a b c a b ( a b c ) ( 3 abc ) ( 4 a bc ) 1 ( ) ( 4 0 x y z 3x y ) ( 3x yz) ( x yz ) Chapter Review
41 41 Use special products for binomials to multiply. a + b a + + b 7. ( 3) ( 3) 8. x ( y 5) x + ( y 5) 9. ( n ) m 1.8 Chapter Review
42 4 10. ( ) 5n 6 m 11. ( ) ( ) x y w 1. ( ) ( ) 3x 5 y + p 1.8 Chapter Review
43 ( c + d ) + ( e f ) 4( c d ) + 3( e 3f ) 14. 4( x x) + 3( x + 1) ( x + x) 5( x 1) 15. ( a + b + 3c d )( 4a b 5c + d ) 1.8 Chapter Review
44 ( x 4y z w )( x 4y + z + w ) x + 5y 17. ( ) 3 4a 3b 18. ( ) Chapter Review
45 45 Use Pascal s Triangle to expand the following: a + b 19. ( ) 7 x y 0. ( ) 6 m + 3n 1. ( ) 5 3x 4y. ( ) Chapter Review
46 46 Use the Binomial Theorem to expand the following: a + b 3. ( ) 4 x y 4. ( ) 5 3a + b 5. ( ) 6 x y 6. ( ) Chapter Review
47 47 Divide using long division. 7. ( x 5 x 3 + x 4) ( x + x ) 8. ( 5y + y 5 + 5) ( y y ) 1.8 Chapter Review
48 48 9. ( a 5 + b 5 ) ( a + b) 30. ( x 6 y 6 ) ( x y ) 1.8 Chapter Review
49 49 Use scientific notation to evaluate. Write your answer in scientific notation and standard notation. 0,000 5,000, ,000,000, ( )( )( ) ( )( ) 3. (,000,000 )( ) Simplify ( ) 1 x + x + ( x + 3) ( y + 0.3) 0.1( 0.3y 0.04) 0.( y ) 1.8 Chapter Review
50 50 Simplify. Your final answer should contain no zero or negative exponents y a b ( a b ) y x y ( x y ) xy x y a b 0.3 a b Chapter Review
51 51 Use special products to multiply ( x y ) + z ( x y ) z a ( b c) a + ( b c ) ( a + 1) 0.0b 0.4( a + 1) + 0.0b y 0.01 ( x + ) 0.1 y ( x + ) 1.8 Chapter Review
52 x y a d ( a 1) + 0.b 46. ( ) 0. x y 1.8 Chapter Review
53 x + y a b ( 0.a 0.3b) ( 0.1x + 0.y ) Chapter Review
54 54 Expand using either Pascal s Triangle or the Binomial Theorem x + y a b x 0.y 53. ( ) 6 0.3a + 0.1b 54. ( ) Chapter Review
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