1. Algebra 1
Section 9.6

2. Dividing Polynomials
To divide a polynomial by a monomial, divide each term of the polynomial by the monomial.
a + b + c d a d b c =

3. Example 1
Divide (12x2 + 20x) by 4x.
12x2 4x
20x =
3x + 5

4. Example 2 8x3 + 16x2 – 4x -4x Divide . 8x3 -4x 16x2 + + ==
-2x2 – 4x + 1

5. Dividing Polynomials
To divide a polynomial by a polynomial, the long division format can be used.

6. Example 3 x + 4 x + 2 x2 + 6x – 9 – ( ) x2 + 2x 4x – 9 – ( ) 4x + 8
– ( )
x2 + 2x 4x
– 9
– ( )
4x + 8
– 17
-17 is the remainder.

7. When writing the final quotient, place the remainder over the divisor.
Example 3
x x2 + 6x – 9
When writing the final quotient, place the remainder over the divisor. 17
x + 2
x + 4 –

8. Dividing Polynomials
Arrange the terms in both the dividend and divisor in descending degree.
Complete the divide, multiply, and subtract procedure.

9. Dividing Polynomials
Repeat step 2 until the degree of the new dividend is less than the degree of the divisor. Place any remainder over the divisor and add the resulting rational expression to the quotient.

10. Dividing Polynomials
Check your results by multiplying your answer by the divisor.

11. Example 5 x2 + 2x + 4 x – 2 x3 – 8 + 0x2 + 0x – ( ) x3 – 2x2 2x2 + 0x
– ( )
x3 – 2x2
2x2
+ 0x
– ( )
2x2 – 4x 4x
– 8
– ( )
4x – 8

12. Example 6 a2 – 2a + 1 3a + 1 3a3 – 5a2 + a + 2 – ( ) 3a3 + a2 -6a2 + a
– ( )
3a3 + a2
-6a2
+ a
– ( )
-6a2 – 2a 3a
+ 2
– ( )
3a + 1 1

13. Homework: pp