MATH SOLVE

5 months ago

Q:
# 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

Accepted Solution

A:

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

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