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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

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Study Guide and Intervention (continued) Dividing Polynomials 5-2 Synthetic Division Use synthetic division to find (23x- 5x2 + 5x - 2) ÷ (x - 1) Thus (2x3 - 5x2 + 5x - 2) ÷ (x - 1) = 2x2 - 3x + 2 Exercises Simplify 1 (3x3 2- 7x + 9x - 14) ÷ (x - 2) 2 (5x3 + 7x2-x - 3) ÷ (x + 1) 2 3 (2x3 + 3x2 - 10x - 3) ÷ (x + 3) 4 (x3 - 8x2 + 19x

How to Divide Polynomials? - GeeksforGeeks

Study Guide and Intervention Dividing Polynomials Use Long Division To divide a polynomial by a monomial use the properties of powers from 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 Example l 1 12p3t2r Simplify 12p3t2r 21p2qtr2 9p3tr 12p3t2r

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5-3 Study Guide and Intervention (continued) Dividing Polynomials Use Synthetic Division a procedure to divide a polynomial by a binomial using coefficients of the dividend and Synthetic division the value of rin the divisor x— r Use synthetic division to find (2 3 — 5x2 + 5x — 2) + (x — 1) Use Long Division To divide a polynomial by a

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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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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[PDF] [PDF] Study Guide and Intervention

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

Lesson 5-1.

Simplify

Use long division to find (x3

The quotient is

Therefore

Exercises

Simplify.

4. (2x

Example 2

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Chapter 5 12 Glencoe Algebra 2

Study Guide and Intervention (continued)

Dividing Polynomials

Synthetic Division

Use synthetic division to find (2

Thus, (2

Exercises

Simplify.

1. (3x

3. (2x

5. (2x

9. (6x

11. (12x

2 -5 5 -2

Step 2

Write the constant

Step 3

Multiply the ? rst coefficient by

2. Write their product under the

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

Step 4

Multiply the sum,

2 -3 2

Step 5

Multiply the sum, 2, by

2. Write the product under the next

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

2 -3 2

2 -3 2 0

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