Factoring Using the Distributive Property

1. Factoring Using the Distributive Property What You'll Learn To use the distributive property to factor Polynomials

2. Distributive Property Remember the distributive property allows us to multiply a monomial with a polynomial 6a(3a -7b) = 18a2 – 42ab We are going to learn how to undo the distributive process, this is known as factoring (expressing the polynomial as a product of a monomial and a polynomial) Think of going from the answer back to the problem.

3. Let’s work a few of these. 1.) (x+2) (x+8) 2.) (x+5) (x-7) 3.) (2x+4) (2x-3)

4. Check your answers. 1.) (x+2) (x+8) = X2+10x+16 2.) (x+5) (x-7) = X2-2x-35 3.) (2x+4) (2x-3) = 4x2+2x-12

5. By learning to use the distributive property, you will be able to multiply any type of polynomials. Example:(x+1)(x2+2x+3) (x+1)(x2+2x+3) = X3+2x2+3x+x2+2x+3

6. Factoring 12mn2 – 18m2n2 First find the greatest number that will divide evenly into 12 and 18 This will be 6 Next find the greatest number of variables common to both terms m and n2 Next divide 6mn2 into each term, You get 2 – 3m. This goes in the parenthesis 6 mn2 (2 – 3m) Check by multiplying back through 6mn2(2 – 3m) = 12mn2 - 18m2n2 We factored it correctly

7. Factor First find the greatest number that will divide evenly into 21 and 14 21x2 – 14x3 Next find the greatest number of variables common to both terms Next divide 7x2 into each term 7 x2 (3 – 2x) Check by multiplying back through 7x2(3 – 2x) = - 14x3 21x2 Factored Correctly

8. (2 m + 3n – 4mn) 2 Factor Try this on your own. 4m + 6n – 8mn How did you do? Got it wrong Click here to return to instruction Got it right Click here to bring on the next problem

9. Factor Try this on your own. 12p3q2 – 18p2q2 + 30pq2 6pq2(2p2 – 3p + 5) How did you do? Got it wrong Click here to return to instruction Got it right Click here to bring on the next problem

10. Classwork/Homework