Question

select the correct answer.
which equation shows function g in factored form?
$g(x) = 2x^2 - 6x - 56$

a. $g(x)=2(x^2 - 3x - 28)$
b. $g(x)=2(x + 4)(x - 7)$
c. $g(x)=2(x - 4)(x + 7)$
d. $g(x)=(2x + 7)(x - 8)$

Explanation:

Step1: Factor out the GCF

First, factor out the greatest common factor (GCF) from the quadratic function \( g(x) = 2x^2 - 6x - 56 \). The GCF of 2, -6, and -56 is 2. So we get:
\( g(x) = 2(x^2 - 3x - 28) \)

Step2: Factor the quadratic inside the parentheses

Now, we need to factor the quadratic \( x^2 - 3x - 28 \). We look for two numbers that multiply to -28 and add up to -3. The numbers are -7 and 4 because \( -7 \times 4 = -28 \) and \( -7 + 4 = -3 \). So we can factor \( x^2 - 3x - 28 \) as \( (x - 7)(x + 4) \).

Step3: Combine the factors

Substituting the factored quadratic back into the expression, we have:
\( g(x) = 2(x + 4)(x - 7) \)

Answer:

B. \( g(x) = 2(x + 4)(x - 7) \)