Question

question 6 of 10
what is the factorization of the trinomial below?
-x² + 2x + 48

a. (x + 6)(x - 8)

b. -1(x + 8)(x + 6)

c. (-x + 6)(x + 8)

d. -1(x - 8)(x + 6)

Explanation:

Step1: Factor out -1

First, factor out -1 from the trinomial:
$-x^2 + 2x + 48 = -1(x^2 - 2x - 48)$

Step2: Factor the quadratic

Now factor $x^2 - 2x - 48$. We need two numbers that multiply to -48 and add to -2. These numbers are -8 and 6 (since $-8 \times 6 = -48$ and $-8 + 6 = -2$). So:
$x^2 - 2x - 48 = (x - 8)(x + 6)$

Step3: Combine with the -1

Substitute back into the factored form from Step1:
$-1(x - 8)(x + 6)$

Answer:

D. $-1(x - 8)(x + 6)$