Question

Select all correct factored forms for the equation x^2+x−42=0 . Answer Choices A .(x−7)(x+6)=0 B. (x+7)(x−6)=0 C. (x−6)(x+7)=0 D. (x+6)(x−7)=0

Answer 1

Both B and C will give you the correct factorization for this equation.

When you factor a quadratic, you are looking for factors of the last number (-42) that add up to the middle coefficient (1). Below are the factors of -42.

1*-42

-1*42

2*-21

-2*21

3*-14

-3*14

6*-7

-6*7

And since these two are the only ones that add up to 1, we use these in parenthesis, creating the following (x - 6)(x + 7) - which is answer C. You also can switch the order due to the laws of multiplication. If you switch them around you get (x + 7)(x - 6) - which is answer B as well.