1. 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

2. Objective
Use long division and synthetic division to divide polynomials.

3. Vocabulary
synthetic division

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

5. 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

6. 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.

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

8. 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 x2 + 8x – 12

9. Check It Out! Example 1a Continued
Step 3 Divide. 5x
+ 1
Notice that 3x times 5x is 15x2. Write 5x above 15x2.
3x x2 + 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.

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

11. 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

12. 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.

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

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