ALGEBRA 1

Lesson 11-3 Warm-Up

ALGEBRA 1

“Dividing Polynomials” (11-3)

How do you divide a polynomial by a monomial?

To divide a polynomial by monomial, divide each term of the polynomial by the monomial individually

Example:

ALGEBRA 1

Divide (18x3 + 9x2 – 15x) by 3x2.

(18x3 + 9x2 – 15x) 3x2÷ = (18x3 + 9x2 – 15x) • .1

3x2

Multiply by the reciprocal of 3x2.

= + –18x3

3x2

9x2

3x2

15x3x2

Use the Distributive Property.

= 6x1 + 3x0 –5x

Use the division rules forexponents.

= 6x + 3 –5x Simplify.

Dividing PolynomialsLESSON 11-3

Additional Examples

ALGEBRA 1

“Dividing Polynomials” (11-3)

How do you divide a polynomial by a binomial?

To divide a polynomial by binomial, use the long division process of Divide, Multiply, Subtract, Bring down (Dad, Mom, Sister, Brother), and repeat as necessary. When dividing, divide by the first term of the binomial only. Just like when dividing numbers, the answer is written as quotient + .

Steps for Dividing a Polynomial by a Polynomial

ALGEBRA 1

“Dividing Polynomials” (11-3)

Example:

Divide by the first term of the binomial, y.

Subtract and bring down the -40.

Divide by the first term of the binomial, y:

ALGEBRA 1

Divide (5x2 + 2x – 3) by (x + 2)

x + 2 5x2 + 2x – 3 Divide: Think 5x2 ÷ x = 5x.

Step 1: Begin the long division process.

5x

Align terms by their degree. So put 5x above 2x of the dividend.

– 8x – 3 Bring down – 3.

5x2 + 10x Multiply: 5x(x + 2) = 5x2 + 10x. Then subtract.

Dividing PolynomialsLESSON 11-3

Additional Examples

ALGEBRA 1

(continued)

Step 2: Repeat the process: Divide, multiply, subtract, bring down.

13 The remainder is 13.

The answer is 5x – 8 + .13

x + 2

5x – 8

x + 2 5x2 + 2x – 3

5x2 + 10x

Divide: –8x ÷ x = – 8– 8x – 3

Multiply: – 8(x + 2) = – 8x – 16. Then subtract.– 8x – 16

Dividing PolynomialsLESSON 11-3

Additional Examples

ALGEBRA 1

The width and area of a rectangle are shown in the

figure below. What is the length?

Since A = w, divide the area by the width to find the length.

The length of the rectangle is (3x2 + 2x + 3) in.

2x – 3 6x3 – 5x2 + 0x – 9 Rewrite the dividend with 0x.

6x3 – 9x2

4x2 + 0x

3x2

4x2 – 6x6x – 9

+ 2x + 3

6x – 90

Dividing PolynomialsLESSON 11-3

Additional Examples

ALGEBRA 1

Divide (–8x – 2 + 6x2) by (–1 + x).

Rewrite –8x – 2 + 6x2 as 6x2 – 8x – 2 and –1 + x as x – 1.Then divide.

The answer is 6x – 2 – .4

x – 1

6x

x – 1 6x2 – 8x – 2

6x2 – 6x

– 2

–2x –2

–2x + 2

–4

Dividing PolynomialsLESSON 11-3

Additional Examples

ALGEBRA 1

Divide.

1. (x8 – x6 + x4) ÷ x2 2. (4x2 – 2x – 6) ÷ (x + 1)

3. (6x3 + 5x2 + 11) ÷ (2x + 3) 4. (29 + 64x3) ÷ (4x + 3)

x6 – x4 + x2 4x – 6

3x2 – 2x + 3 +2

2x + 3 16x2 – 12x + 9 +2

4x + 3

Dividing PolynomialsLESSON 11-3

Lesson Quiz