Question

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

Answer 1

D. Latisha

ex: edg2020/2021

Answer 2

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