1. Dividing Polynomials Using Factoring (11-5)
Objective: Divide a polynomial by a monomial. Divide a polynomial by a binomial.

2. Divide Polynomials by Monomials.
To divide a polynomial by a monomial, divide each term of the polynomial by the monomial.
Divide Polynomials by Monomials.

3. Example 1 2x – 9 Find each quotient. (4x2 – 18x) ÷ 2x
(2y2 – 3y – 9) ÷ 3y
2x – 9
Example 1

4. Check Your Progress Choose the best answer for the following.
Find (48z2 + 18z) ÷ 6z.
8z + 18z
8z + 18
8z + 3
42z + 12
Check Your Progress

5. Check Your Progress Choose the best answer for the following.
Find (-8x2 + 6x – 28) ÷ 4x.
-2x + 6x - 28
-2x + 3/2 – 7
-12x + 2 – 24/x
-2x + 3/2 – 7/x
Check Your Progress

6. Divide Polynomials by Binomials
You can also divide polynomials by binomials.
When a polynomial can be factored and common factors can be divided out, write the division as a fraction and simplify.
Divide Polynomials by Binomials

7. Find (2r2 + 5r – 3) ÷ (r + 3).
b = 5
ac = -6
Example 2
2r – 1

8. Check Your Progress Choose the best answer for the following.
Find (2c2 – 3c – 9) ÷ (c – 3).
2c + 3
c + 3
c – 3
2c2 – 3c - 9
b = -3
ac = -18
Check Your Progress

9. Divide Polynomial by Binomials
If the polynomial cannot be factored or if there are no common factors by which to divide, you must use long division.
Divide Polynomial by Binomials

10. Example 3 Find (x2 + 7x – 15) ÷ (x – 2) by using long division. x + 9

11. Check Your Progress Choose the best answer for the following.
Find (y2 – 4y + 5) ÷ (y – 3) by using long division.
y – 2
y – 1
y + 5 y
– 1
y2 – 3y
-1y + 5
-1y + 3 2
Check Your Progress

12. The area of a rectangle is represented by 3x + 90
The area of a rectangle is represented by x Its length is (x – 3). Find (3x + 90) ÷ (x – 3) to find the width of the rectangle. 3
3x – 9 99
Example 4

13. Check Your Progress Choose the best answer for the following. 8
The area of a triangle is represented by 8x The height is 2x Find 2(8x + 21) ÷ (2x + 3) to find the base of the triangle.
8 +
6 +
4 + 8
16x + 24 18
Check Your Progress

14. Dividing Polynomials by Binomials
When a dividend is written in standard form and a power is missing, add a term of that power with a coefficient of zero.
Dividing Polynomials by Binomials

15. Example 5 Find (x3 – 34x + 45) ÷ (x – 5). x2 + 5x – 9 x2 + 5x – 9
Example 5

16. Check Your Progress Choose the best answer for the following.
Find (b3 – 6b2 + 32) ÷ (b – 4).
b2 – 2b – 8
b – 8
b2 – 8 b2 b2
– 2b
– 8
b3 – 4b2
-2b2 + 0b
-2b2 + 8b
-8b + 32
-8b + 32
Check Your Progress