Answer:
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.
