Did I solve factoring with a zero product property correctly

Question

Did I solve this problem correctly by using factoring and the zero-product property?

 

z(z - 1)(z + 3) = 0

 

step 1   z( z - 1) = 0     or  z( z + 3) =

step 2   z( z) = 1              (z) z - -3

 

   check:

 

           (1 -1 ) (-3 + 3)                     (-3 -1) (-3 + 3)

        1 (-3 + 3 + 3 + -3)  =0             -3(9 + -9 + 3 + -3) = 0    

 

 

 

How do I solve x^2 - x - 10 = 2   using factoring and the zero product property

Answer 1

You want to set each factor equal to zero and then solve

 

Step 1: z = 0 or z-1 = 0 or z+3=0

Step 2: z = 0 or z = 1 or z = -3

 

For the other problem, you must make the right side 0 by subtracting 2 from both sides to get

 

x² - x - 12 = 0

 

Now when possible, to factor ax²+bx+c, you want to find two integers m,n with sum b and product ac.

 

Here we have m+n = -1 and mn = -12. We can take m = 3, n = -4. This gives

 

x² - x - 12 = x² + 3x - 4x - 12 = x(x+3) - 4(x + 3) = (x - 4)(x + 3).

 

Now we have (x - 4)(x + 3) = 0

 

Step 1: x - 4 = 0 or x + 3 = 0

Step 2: x = 4 or x = -3