[PDF] 5-2 - Study Guide and Intervention





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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.



Study Guide and Intervention

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 ...



5-2 - Study Guide and Intervention

Glencoe Algebra 2. Study Guide and Intervention. Dividing Polynomials. 5-2. Long Division To divide a polynomial by a monomial use the skills learned in.



8-5 Study Guide and Intervention.pdf

Multiplying. 3(a + b) = 3a + 3b x(y ? z) = xy — XZ. Use the Distributive Property to Factor The Distributive Property has been used to multiply a polynomial by 



8-2 Study Guide and Intervention - Multiplying a Polynomial by a

Polynomial Multiplied by Monomial The Distributive Property can be used to multiply a polynomial by a monomial. You can multiply horizontally or vertically.



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track of terms in the product is to use the FOIL method as illustrated in Example 2. Example 1: Find (x + 3)(x – 4). Horizontal Method. (x + 3)( 



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PERIOD. Lesson 8-2. PDF Pass. Chapter 8. 13. Glencoe Algebra 1. Study Guide and Intervention (continued). Multiplying a Polynomial by a Monomial.



Chapter 8 cover

Chapter 8 Polynomials Multiply Monomials A monomial is a number a variable



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PERIOD. Chapter 8. 14. Glencoe Algebra 1. Skills Practice. Multiplying a Polynomial by a Monomial. Find each product. 1. a(4a + 3). 2. -c(11c + 4).



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(





00i ALG1 A CRM C08 TP 660282 - Weebly

11 To solve an equation such as x2 = 8 + 2x take the square root of both sides D 12 The polynomial 3r2-r - 2 can not be factored because the coefficient of r2 is not 1 D 13 AThe polynomial t2 + 16 is not factorable 14 The numbers 16 64 and 121 are perfect squares A 8 001_014_ALG1_A_CRM_C08_CR_660282 indd 3 12/20/10 7:02 PM Answers



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

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Lesson X-2

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Lesson 5-2

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Chapter 5 11 Glencoe Algebra 2

Study Guide and Intervention

Dividing Polynomials

5-2 Long Division To divide a polynomial by a monomial, use the skills learned in

Lesson 5-1.

To divide a polynomial by a polynomial, use a long division pattern. Remember that only like terms can be added or subtracted.

Simplify

12 p 3 t 2 r - 21 p 2 qt r 2 - 9 p 3 tr 3 p 2 tr 12 p 3 t 2 r - 21 p 2 qt r 2 - 9 p 3 tr 3 p 2 tr 12 p 3 t 2 r 3 p 2 tr 21 p
2 qt r 2 3 p 2 tr 9 p 3 tr 3 p 2 tr = 12 3 p (3 - 2) t (2 - 1) r (1 - 1) 21
3 p (2 - 2) qt (1 - 1) r (2 - 1) 9 3 p (3 - 2) t (1 - 1) r (1 - 1) = 4pt -7qr - 3p

Use long division to find (x3

- 8x 2 + 4x - 9) ÷ (x - 4). x 2 - 4x - 12 x - 4 x 3 - 8x 2 + 4x - 9 (-) x 3 - 4x 2 -4x 2 + 4x (-)-4x 2 + 16x -12x - 9 (-)-12x + 48 -57

The quotient is

x 2 - 4x - 12, and the remainder is -57.

Therefore

x 3 - 8 x 2 + 4x - 9 x - 4 = x 2 - 4x - 12 - 57
x - 4

Exercises

Simplify.

1. 18 a 3 + 30 a 2 3a 2. 24
m n 6 - 40 m 2 n 3 4 m 2 n 3 3. 60 a
2 b 3 - 48 b 4 + 84 a 5 b 2 12 a b 2

4. (2x

2 - 5x - 3) ÷ (x - 3) 5. (m 2 - 3m - 7) ÷ (m + 2) 6. (p 3 - 6) ÷ (p - 1) 7. (t 3 - 6t 2 + 1) ÷ (t + 2) 8. (x 5 - 1) ÷ (x - 1) 9. (2x 3 - 5x 2 + 4x - 4) ÷ (x - 2)Example 1

Example 2

6 a 2 + 10a 6 n 3 m - 105ab - 4 b 2 a + 7a 4 2 x + 1m - 5 + 3 m + 2 p 2 + p + 1 - 5 p - 1 t 2 - 8t + 16 - 31
t + 2 x 4 + x 3 + x 2 + x + 12x 2 - x + 2

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

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Chapter 5 12 Glencoe Algebra 2

Study Guide and Intervention (continued)

Dividing Polynomials

5-2

Synthetic Division

Use synthetic division to find (2

x 3 - 5x 2 + 5x - 2) ÷ (x - 1).

Thus, (2

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

Exercises

Simplify.

1. (3x

3 - 7x 2 + 9x - 14) ÷ (x - 2) 2. (5x 3 + 7x 2 - x - 3) ÷ (x + 1)

3. (2x

3 + 3x 2 - 10x - 3) ÷ (x + 3) 4. (x 3 - 8x 2 + 19x - 9) ÷ (x - 4)

5. (2x

3 + 10x 2 + 9x + 38) ÷ (x + 5) 6. (3x 3 - 8x 2 + 16x - 1) ÷ (x - 1) 7. (x 3 - 9x 2 + 17x - 1) ÷ (x - 2) 8. (4x 3 - 25x 2 + 4x + 20) ÷ (x - 6)

9. (6x

3 + 28x 2 - 7x + 9) ÷ (x + 5) 10. (x 4 - 4x 3 + x 2 + 7x - 2) ÷ (x - 2)

11. (12x

4 + 20x 3 - 24x 2 + 20x + 35) ÷ (3x + 5)

Synthetic divisiona procedure to divide a polynomial by a binomial using coefficients of the dividend and

the value of r in the divisor x - r

Step 1Write the terms of the dividend so that the degrees of the terms are in descending order. Then write just the coefficients.2x

3 - 5x 2 + 5x - 2

2 -5 5 -2

Step 2

Write the constant

r of the divisor x - r to the left, In this case, r = 1. Bring down the ? rst coefficient, 2, as shown.1 2 -5 5 -2 2

Step 3

Multiply the ? rst coefficient by

r , 1 2

2. Write their product under the

second coefficient. Then add the product and the second coefficient:

5 + 2 = - 3.1 2 -5 5 -2

2 2 -3

Step 4

Multiply the sum,

3, by r : -3 1 -3. Write the product under the next coefficient and add: 5 (-3) = 2.1 2 -5 5 -2 2 -3

2 -3 2

Step 5

Multiply the sum, 2, by

r : 2 1

2. Write the product under the next

coefficient and add:

2 + 2 = 0. The remainder is 0.1 2 -5 5 -2

2 -3 2

2 -3 2 0

3 x 2 - x + 75x 2 + 2x - 3 2 x 2 - 3x - 1x 2 - 4x + 3 + 3 x - 4 2 x 2 + 9 - 7 x + 5 3x 2 - 5x + 11 + 10 x - 1 x 2 - 7x + 3 + 5 x - 2 4x 2 - x - 2 + 8 x - 6 6 x 2 - 2x + 3 - 6 x + 5 x 3 - 2x 2 - 3x + 1 4 x 3 - 8x + 20 + 65
3 x + 5

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