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9-2 Factor using distributive property (part 1)

9-2 Factor using distributive property (part 1). Factoring a polynomial means… Find its completely factored form using the distributive property. What are t he steps?. Find the GCF Divide out the GCF Put GCF on outside of ( ) Leave everything else on the inside of ( ).

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9-2 Factor using distributive property (part 1)

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  1. 9-2 Factor using distributive property(part 1) Factoring a polynomial means… Find its completely factored form using the distributive property

  2. What are the steps? • Find the GCF • Divide out the GCF • Put GCF on outside of ( ) • Leave everything else on the inside of ( )

  3. Let's look at 12a2 + 16a

  4. Let's look at 12a2 + 16a 12a2 + 16a / \ / \ 2 6 2 8 / \ / \ 2 3 2 4 /\ 2 2

  5. 1. Find the GCF 12a2 + 16a / \ / \ 2 6 2 8 12a2 = 2*2*3*a*a / \ / \ 16a = 2*2*2*2*a 2 3 2 4 /\ GCF = 4a 2 2

  6. 2. Divide out GCF 12a2 + 16a 4a 4a leaves 3a + 4

  7. 3. Put GCF on outside of ( )4. Leave everything else inside the ( ) So, 12a2 + 16a = 4a ( 3a + 4 )

  8. How about 18cd2 + 12c2d + 9cd First find the GCF Then divide it out Write the factors (GCF on outside and rest on inside)

  9. How about 18cd2 + 12c2d + 9cd 18cd2 + 12c2d + 9cd / \ / \ / \ 2 9 2 6 3 3 / \ / \ 3 3 2 3 18cd2 = 2*3*3*c* d*d GCF 12c2d = 2*3*3*c*c*d 3cd 9cd = 3*3*c* d

  10. So, 18cd2 + 12c2d + 9cd 3cd 3cd3cd 3cd ( 6d + 4c + 3 ) GCF ( what’s left)

  11. How do we solve equations that contain polynomials? 1.Move all terms to the left of the (=) so that the polynomial is equal to zero. 2. Factor the left side of the polynomial. 3. Use the multiplication property of zero to solve. (the multiplication property of zero says: if two factors multiply to equal zero, then one or both factors must be equal to zero)

  12. Let's look at x2 = 7x Step 1 (move the 7x) X2 = 7x -7x -7x x2 – 7x = 0

  13. Let's look at x2 = 7x Step 1 (move the 7x) Step 2 (factor x2 – 7x) X2 = 7x x2 = x * x -7x -7x 7x = 7 * x x2 – 7x = 0 GCF = x so we have x ( x – 7 ) = 0

  14. Let's look at x2 = 7x Step 1 (move the 7x) Step 2 (factor x2 – 7x) X2 = 7x x2 = x * x -7x -7x 7x = 7 * x x2 – 7x = 0 GCF = x so we have x ( x – 7 ) = 0 Step 3 (set each factor equal to zero and solve) x = 0 or (x – 7 ) = 0 +7 +7 x = 7

  15. Step 1 (move the 7x) Step 2 (factor x2 – 7x) X2 = 7x x2 = x * x -7x -7x 7x = 7 * x x2 – 7x = 0 GCF = x so we have x ( x – 7 ) = 0 Step 3 (set each factor equal to zero and solve) x = 0 or (x – 7 ) = 0 +7 +7 x = 7 So, the solution set is {0 , 7}

  16. Your turn to try some… Factor the polynomial Solve each equation • 5x + 30y 4. x ( x – 24 ) = 0 • 14gh – 18h 5. 2x2 = 5x • 8bc2 + 24bc 6. 3z2 + 2z = 0

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