Factor completely.

x²-3x-28

A. (x - 7) (x+4)

B. (x + 7) (x-4)

C. (x + 14) (x-2)

D. (x + 14) (x + 2)

A. (x - 7) (x+4)

Step-by-step explanation:

To factor x²-3x-28, you need two numbers that add to get - 3 and also multiply to get - 28.

p + q = - 3 At least one of p and q must be negative.

p * q = - 28

Find the factors of - 28, then decide which two also add to get - 3.

Trial and error:

-2 and 14 multiply to be - 28. But when added, they are 12, not 3.

If you multiply 7 and - 4, the product is - 28. If you add them, the are 3, not - 3.

Multiply - 7 and 4, the product is - 28. Added together, the sum is - 3.

x² - 3x - 28 = (x + q) (x + p)

q = - 7

p = 4

x² - 3x - 28 = (x - 7) (x + 4)

Check your work: Expand (x - 7) (x+4). Use FOIL (first, outside, inside, last) to multiply every term in one bracket by every term in the other bracket.

(x - 7) (x+4)

= x² + 4x - 7x - 28 Combined like terms 4x and - 7x

= x² - 3x - 28 Same as question, so the answer is correct.