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8-2 Study Guide and Intervention.pdf

NAME Answer Key. 8-2 Study Guide and Intervention. Multiplying a Polynomial by a Monomial. Example 1: Find ?3x² (4x² + 6x ? 8). www. Horizontal Method.



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Polynomial Multiplied by Monomial The Distributive Property can be used to multiply a -11z3 + 4z2 - z. 28x2 - 6x - 12. Example 1. Example 2. 8-2 ...



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NAME DATE PERIOD 8-2 Study Guide and Intervention - Weebly

multiply a polynomial by a monomial You can multiply horizontally or vertically Sometimes multiplying results in like terms The products can be simplified by combining like terms Find -3x2(4x2 + 6x-8) Horizontal Method-3x2(4x2 + 6x - 8) 2= -3x 2(4x) + (-3x)(6x) - (-3x2)(8) = -12x4 3+ (-18x) - (-24x2) = 3-12x4 2- 18x + 24x Vertical Method



8-2 Study Guide and Intervention - Amazon Web Services Inc

Polynomial Multiplied by Monomial The Distributive Property can be used to multiply a polynomial by a monomial You can multiply horizontally or vertically Sometimes multiplying results in like terms The products can be simplified by combining like terms Example 1: Find –3 (4 Horizontal Method + 6x – 8) Example 2: Simplify –2(4 + 5x) – x(





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Multiplying a Polynomial and a Monomial - Effortless Math

Answers Multiplying a Polynomial and a Monomial 1) T2+3 T 2) ?8 T+16 2 3) 24 T+2 T 4) 2? T 2+3 T 5) 9 T2?6 T 6) 15 T?30 U 7) 56 T2?32 T 8) 227 T+6 T U 9) 26 T+12 T U 2 10) 18 T2+36 T U T 11) 36 T2+108 T 18 12) 22 T2?121 T U 24 13) 12 T2?12 T U 6 14) 6 T2?12 T U+6 T 4 15) 215 T3+10 T U 30 16) 52 T2+104 T U 17) 10 T2?45 U2

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Chapter 8 12 Glencoe Algebra 1

Study Guide and Intervention

Multiplying a Polynomial by a Monomial

Polynomial Multiplied by Monomial The Distributive Property can be used to multiply a polynomial by a monomial. You can multiply horizontally or vertically. Sometimes multiplying results in like terms. The products can be simplified by combining like terms.

Find -3x

2 (4 x 2 + 6x - 8).

Horizontal Method

3 x 2 (4 x 2 + 6x - 8) -3 x2 (4 x 2 ) + (-3x 2 )(6 x ) - (-3x 2 )(8) -12x 4 + (-18x 3 ) - (-24x 2 -12x 4 - 18x 3 + 24x 2

Vertical Method

4x 2 + 6x - 8 ) -3x 2 -12x 4 - 18x 3 + 24x 2

The product is

12 x 4 - 18x 3 + 24x 2 . Simplify - 2(4 x2 + 5x) x(x 2 + 6x). 2(4 x 2 + 5x) - x( x 2 + 6x) -2(4x 2 ) + (-2)(5x) + (-x)(x 2 ) + (-x)(6x) -8x 2 + (-10x) + (-x 3 ) + (-6x 2 (-x 3 ) + [-8x 2 + (-6x 2 )] + (-10x) -x3 - 14x 2 - 10x

Exercises

Find each product.

1. x(5x + x

2

2. x(4x

2 + 3x + 2) 3. -2xy(2y + 4x 2 5x 2 + x 3 4x 3 3x 2

2x -4xy

2 - 8x 3 y

4. -2g(g

2 - 2g + 2) 5. 3x(x 4 + x 3+ x 2

6. -4x(2x

3 - 2x + 3) -2g 3 + 4g 2 - 4g 3x 5 + 3x 4 + 3x 3 -8x 4 8x 2 12x

7. -4ax(10 + 3x) 8. 3y(-4x - 6x

3

2y) 9. 2x

2 y 2 (3 xy + 2y + 5x) -40ax - 12ax

2 -12xy - 18x

3 y - 6y 2 6x 3 y 3 + 4x 2 y 3 + 10x 3 y 2

Simplify each expression.

10. x(3x - 4) - 5x 11. -x(2x

2 - 4x) - 6x 2 3x 2 - 9x -2x 3 - 2x 2

12. 6a(2a - b) + 2a(-4a + 5b) 13. 4r(2r

2

3r + 5) + 6r(4r2

+ 2r + 8) 4a 2 + 4ab 32r 3 + 68r

14. 4n(3n

2 + n - 4) - n(3 - n) 15. 2b(b 2 + 4b + 8) - 3b(3b 2 + 9b - 18) 12n 3 + 5n 2 - 19n -7b 3 - 19b 2 + 70b

16. -2z(4z

2 - 3z + 1) - z(3z

2 + 2z - 1) 17. 2(4x 2 - 2x) - 3(-6x 2 + 4) + 2x(x - 1) -11z 3 + 4z 2 - z 28x 2 - 6x - 12

Example 1Example 2

8-2 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Lesson 8-2

Chapter 8 13 Glencoe Algebra 1

Study Guide and Intervention (continued)

Multiplying a Polynomial by a Monomial

Solve Equations with Polynomial Expressions Many equations contain polynomials that must be added, subtracted, or multiplied before the equation can be solved.

Solve 4(n - 2) + 5n = 6(3 - n) + 19.

4( n - 2) + 5n = 6(3 - n) + 19

Original equation

4n - 8 + 5n = 18 - 6n + 19 Distributive Property

9n - 8 = 37 - 6n Combine like terms.

15 n - 8 = 37 Add 6n to both sides. 15 n = 45 Add 8 to both sides. n = 3 Divide each side by 15.

The solution is 3.

Exercises

Solve each equation.

1. 2(a - 3) = 3(-2a + 6)

3 2. 3(x + 5) - 6 = 18 3

3. 3x(x - 5) - 3x

2 = -30 2 4. 6(x 2 + 2x) = 2(3x 2 + 12) 2

5. 4(2p + 1) - 12p = 2(8p + 12) -1 6. 2(6x + 4) + 2 = 4(x - 4) - 3

1 4

7. -2(4y - 3) - 8y + 6 = 4(y - 2)

1 8. x(x + 2) - x(x - 6) = 10x - 12 6

9. 3(x

2 - 2x) = 3x 2 + 5x - 11 1 10. 2(4x + 3) + 2 = -4(x + 1) -1

11. 3(2h - 6) - (2h + 1) = 9 7 12. 3(y + 5) - (4y - 8) = -2y + 10 -13

13. 3(2a - 6) - (-3a - 1) = 4a - 2 3 14. 5(2x

2 - 1) - (10x 2 - 6) = -(x + 2) -3

15. 3(x + 2) + 2(x + 1) = -5(x - 3)

7 10

16. 4(3p

2 + 2p) - 12p 2 = 2(8p + 6) - 3 2

Example

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