Question

Factor the expression x^2−2x−48. Select the correct choice below and, if necessary, fill in the answer box.

A. x^2−2x−48=(x−8)(x+6)
B. x^2−2x−48=(x+8)(x−6)
C. x^2−2x−48=(x−6)(x+8)
D. x^2−2x−48=(x+6)(x−8)

Answer 1

To factor the quadratic expression x^2−2x−48, one must find two numbers that multiply to −48 and add to −2, which are −8 and +6. Therefore, the factored form is (x − 8)(x + 6).

Step-by-step explanation:

The expression x^2−2x−48 can be factored by finding two numbers that multiply to −48 and add up to −2. We are looking for factors of −48 that when added give us −2. The pair of numbers that fit this condition are −8 and +6. Thus, the expression can be factored as:

x^2−2x−48 = (x − 8)(x + 6).

The correct choice is A: x^2−2x−48 = (x − 8)(x + 6).