1. 8-5 Factoring Using the distributive property
Goals:
Use the distributive property to factor a polynomial.
Solve polynomial equations by factoring.
Eligible Content: A

2. Vocabulary Monomial – a polynomial that only has one term.
Greatest Common Factor – biggest term that all terms are divisible by.

3. The Greatest Common Factor
The GCF is
the biggest number the coefficients are divisible by
the variable with the smallest exponent.

4. Find the GCF
5x2 , 15x3 , 35x 5, 15 and 35 are all divisible by 5 x2, x3 , and x are all divisible by x GCF is 5x

5. Examples Find the GCF. 2x2 and 16x3 32x5, 48x2, 24x3 45x4, 18x, 27x3
4a2b, 8ab2, 2ab
12x3y2, 18x4y3, 9x2y2
2x2
8x2 9x
2ab
3x2y2

6. factoring using the distributive Property
Divide the polynomial by the GCF
Remember: when dividing variables you should subtract the exponents!!!!
Factor the remaining polynomial if possible.

7. Factor completely: 6x3 – 36x2 + 48x
GCF = 6x
6x3 – 36x2 + 48x
6x 6x x
6x( )
6x( )( ) x2
– 6x
+ 8
x – 2
x – 4

8. Examples 14x4y3 – 21x2y 2x3y2 + 8x 4x3 + 20x2 + 24x 45x4 – 20x2
2x(x2y2 + 4)
4x(x + 2)(x + 3)
5x2(3x + 2)(3x – 2)
5x2(x + 3)(x – 6)

9. Use the Distributive Property to factor the polynomial
3x2y + 12xy2.
A. 3xy(x + 4y)
B. 3(x2y + 4xy2)
C. 3x(xy + 4y2)
D. xy(3x + 2y)

10. Use the Distributive Property to factor the polynomial
3ab2 + 15a2b2 + 27ab3.
A. 3(ab2 + 5a2b2 + 9ab3)
B. 3ab(b + 5ab + 9b2)
C. ab(b + 5ab + 9b2)
D. 3ab2(1 + 5a + 9b)

11. Practice
Worksheet – 8-5 Factoring Using the Distributive Property”

12. Solve the Equations 8x3 – 18x = 0 2x3 – 10x2 + 8x = 0
x = 0, 1.5 or -1.5
x = 0, 1 or 4

13. Homework
Page #1-4, 15-20