Warm Up Divide using long division. 1. 161 ÷ 7 23 2. 12.18 ÷ 2.1 5.8 6x – 15y 3 3. 2x + 5y 7a2 – ab a 4. 7a – b

Objective Use long division and synthetic division to divide polynomials.

Vocabulary synthetic division

Polynomial long division is a method for dividing a polynomial by another polynomials of a lower degree. It is very similar to dividing numbers.

Example 1: Using Long Division to Divide a Polynomial Divide using long division. (–y2 + 2y3 + 25) ÷ (y – 3) Step 1 Write the dividend in standard form, including terms with a coefficient of 0. 2y3 – y2 + 0y + 25 Step 2 Write division in the same way you would when dividing numbers. y – 3 2y3 – y2 + 0y + 25

Example 1 Continued Step 3 Divide. 2y2 + 5y + 15 Notice that y times 2y2 is 2y3. Write 2y2 above 2y3. y – 3 2y3 – y2 + 0y + 25 –(2y3 – 6y2) Multiply y – 3 by 2y2. Then subtract. Bring down the next term. Divide 5y2 by y. 5y2 + 0y –(5y2 – 15y) Multiply y – 3 by 5y. Then subtract. Bring down the next term. Divide 15y by y. 15y + 25 Multiply y – 3 by 15. Then subtract. –(15y – 45) 70 Find the remainder.

Example 1 Continued Step 4 Write the final answer. –y2 + 2y3 + 25 y – 3 = 2y2 + 5y + 15 + 70 y – 3

Check It Out! Example 1a Divide using long division. (15x2 + 8x – 12) ÷ (3x + 1) Step 1 Write the dividend in standard form, including terms with a coefficient of 0. 15x2 + 8x – 12 Step 2 Write division in the same way you would when dividing numbers. 3x + 1 15x2 + 8x – 12

Check It Out! Example 1a Continued Step 3 Divide. 5x + 1 Notice that 3x times 5x is 15x2. Write 5x above 15x2. 3x + 1 15x2 + 8x – 12 –(15x2 + 5x) Multiply 3x + 1 by 5x. Then subtract. Bring down the next term. Divide 3x by 3x. 3x – 12 –(3x + 1) Multiply 3x + 1 by 1. Then subtract. –13 Find the remainder.

Check It Out! Example 1a Continued Step 4 Write the final answer. 15x2 + 8x – 12 3x + 1 = 5x + 1 – 13 3x + 1

Check It Out! Example 1b Divide using long division. (x2 + 5x – 28) ÷ (x – 3) Step 1 Write the dividend in standard form, including terms with a coefficient of 0. x2 + 5x – 28 Step 2 Write division in the same way you would when dividing numbers. x – 3 x2 + 5x – 28

Check It Out! Example 1b Continued Step 3 Divide. x + 8 Notice that x times x is x2. Write x above x2. x – 3 x2 + 5x – 28 –(x2 – 3x) Multiply x – 3 by x. Then subtract. Bring down the next term. Divide 8x by x. 8x – 28 –(8x – 24) Multiply x – 3 by 8. Then subtract. –4 Find the remainder.

Check It Out! Example 1b Continued Step 4 Write the final answer. x2 + 5x – 28 x – 3 = x + 8 – 4 x – 3

Holt Chapter 6 Section 3 Page 426 #2-4, 13-18 Homework! Holt Chapter 6 Section 3 Page 426 #2-4, 13-18