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## 9-2 Factor using distributive property (part 1)

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**9-2 Factor using distributive property(part 1)**Factoring a polynomial means… Find its completely factored form using the distributive property**What are the steps?**• Find the GCF • Divide out the GCF • Put GCF on outside of ( ) • Leave everything else on the inside of ( )**Let's look at 12a2 + 16a**12a2 + 16a / \ / \ 2 6 2 8 / \ / \ 2 3 2 4 /\ 2 2**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**2. Divide out GCF**12a2 + 16a 4a 4a leaves 3a + 4**3. Put GCF on outside of ( )4. Leave everything else**inside the ( ) So, 12a2 + 16a = 4a ( 3a + 4 )**How about 18cd2 + 12c2d + 9cd**First find the GCF Then divide it out Write the factors (GCF on outside and rest on inside)**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**So,**18cd2 + 12c2d + 9cd 3cd 3cd3cd 3cd ( 6d + 4c + 3 ) GCF ( what’s left)**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)**Let's look at x2 = 7x**Step 1 (move the 7x) X2 = 7x -7x -7x x2 – 7x = 0**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**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**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}**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