1. Goals: Use the distributive property to factor a polynomial. Solve polynomial equations by factoring. Eligible Content: A1.1.1.5.2

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

3.  The GCF is  the biggest number the coefficients are divisible by  the variable with the smallest exponent.

4. 5x 2, 15x 3, 35x 5, 15 and 35 are all divisible by 5 x 2, x 3, and x are all divisible by x GCF is 5x

5. Find the GCF. 1. 2x 2 and 16x 3 2. 32x 5, 48x 2 and 24x 3 3. 45x 4, 18x and 27x 3  2x 2  8x 2  9x

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

7.  GCF = 6x 6x 3 – 36x 2 + 48x 6x 6x 6x 6x( ) 6x( )( ) x2x2 – 6x+ 8 x – 2x – 4

8. 1. 14x 4 – 21x 2 2. 2x 3 + 8x 3. 4x 3 + 20x 2 + 24x 4. 45x 4 – 20x 2 5. 5x 4 – 15x 3 – 90x 2  7x 2 (2x 2 – 3)  2x(x 2 + 4)  4x(x + 2)(x + 3)  5x 2 (3x + 2)(3x – 2)  5x 2 (x + 3)(x – 6)

9.  Worksheet – 8-5 Factoring Using the Distributive Property”

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

11. A.3(ab 2 + 5a 2 b 2 + 9ab 3 ) B.3ab(b + 5ab + 9b 2 ) C.ab(b + 5ab + 9b 2 ) D.3ab 2 (1 + 5a + 9b) Use the Distributive Property to factor the polynomial 3ab 2 + 15a 2 b 2 + 27ab 3.

12. 1. 8x 3 – 18x = 0 2. 2x 3 – 10x 2 + 8x = 0  x = 0, 1.5 or -1.5  x = 0, 1 or 4

13.  Page 497-498 #1-4, 15-20