Question

Which expression is the completely factored form of the expression x2 − 3x − 28? A. (x − 7)(x + 4)

B. (x + 7)(x − 4)
C. (x + 14)(x − 2)
D. (x + 14)(x + 2)

Answer 1

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

Answer 2

A

Explanation:

The coefficient of the x^2 term is 1 and the constant term is -28. In order to factor this, we need to find factor pairs of 1 and -28 that will add together in some way to produce -3, the coefficient of the x term.

The factors of 1 are obviously just 1 and 1. The factors of -28 are (1, -28), (2, -14), (4, -7), (-4, 7), (-2, 14), and (-1, 28). Upon examination, we see that if we have the factor pairs (4, -7), from -28, and (1, 1), from 1, we can make -3:

4 * 1 + (-7) * 1 = 4 - 7 = -3

So, we know that our factors are: x + 4 and x + -7, or x - 7. Thus, the answer is A.

Hope this helps!