Four students are verifying that x2 + x– 12 = (x – 3)(x + 4). Their conclusions are presented in the table. Which student correctly verified that x2 + x – 12 = (x – 3)(x + 4)? Damien Lauryn Rico Latisha

We want to verify that x² + x - 12 = (x - 3)(x + 4)

We can prove this by factoring the left side and showing that it is equal to the Right side.

We should find factors of -12 that sum to +1.
-12 = 1 x -12   Sum = 1 - 12 = -11    No
-12 = 2 x -6    Sum = 2 - 6 = -4    No
-12 = 3 x -4    Sum = 3 - 4 = -1     No
-12 = 4 x -3    Sum = 4 - 3 = 1      Yes

Therefore
x² + x - 12 = (x - 3)(x + 4) which is equal to the Right side.

Latisha is correct because
4(-3) = -12, and
-3 + 4 = 1

Answer: Latisha