Lesson 11-3 Warm-Up

“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:

Multiply by the reciprocal of 3x2. Dividing Polynomials LESSON 11-3 Additional Examples Divide (18x3 + 9x2 – 15x) by 3x2. (18x3 + 9x2 – 15x) 3x2 ÷ = (18x3 + 9x2 – 15x) • . 1 Multiply by the reciprocal of 3x2. = + – 18x3 3x2 9x2 15x Use the Distributive Property. = 6x1 + 3x0 – 5 x Use the division rules for exponents. = 6x + 3 – 5 x Simplify.

“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

“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:

Step 1: Begin the long division process. Dividing Polynomials LESSON 11-3 Additional Examples 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. 5x2 + 10x Multiply: 5x(x + 2) = 5x2 + 10x. Then subtract. – 8x – 3 Bring down – 3.

Step 2: Repeat the process: Divide, multiply, subtract, bring down. Dividing Polynomials LESSON 11-3 Additional Examples (continued) Step 2: Repeat the process: Divide, multiply, subtract, bring down. 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 13 The remainder is 13. The answer is 5x – 8 + . 13 x + 2

Since A = w, divide the area by the width to find the length. Dividing Polynomials LESSON 11-3 Additional Examples 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. 6x3 – 9x2 4x2 + 0x 3x2 4x2 – 6x 6x – 9 + 2x + 3 6x – 9 2x – 3 6x3 – 5x2 + 0x – 9 Rewrite the dividend with 0x. The length of the rectangle is (3x2 + 2x + 3) in.

Divide (–8x – 2 + 6x2) by (–1 + x). Dividing Polynomials LESSON 11-3 Additional Examples Divide (–8x – 2 + 6x2) by (–1 + x). Rewrite –8x – 2 + 6x2 as 6x2 – 8x – 2 and –1 + x as x – 1. Then divide. 6x x – 1 6x2 – 8x – 2 6x2 – 6x – 2 –2x –2 –2x + 2 –4 The answer is 6x – 2 – . 4 x – 1

1. (x8 – x6 + x4) ÷ x2 2. (4x2 – 2x – 6) ÷ (x + 1) Dividing Polynomials LESSON 11-3 Lesson Quiz 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