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

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Mathematics

Wiggles

23 July, 21:28

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

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Jones · 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.