Question

Which equation shows function g in factored form?

A) g(x) = 2(x + 4)(x - 7)
B) g(x) = 2(x - 4)(x + 7)
C) g(x) = (2x + 7)(x - 8)
D) g(x) = 2(x^2 - 3x - 28)

Answer 1

Option A shows function g in factored form, which is g(x) = 2(x + 4)(x - 7) after factoring the quadratic expression given in option D.

Step-by-step explanation:

The student is asking about which equation represents the function g in factored form. To determine the factored form, we need to look for an equation that can be written as a product of linear factors. Option D cannot be the factored form because it still shows a quadratic expression in standard form (ax2 + bx + c). Let's factor the quadratic expression in option D:

g(x) = 2(x2 - 3x - 28)

which factors to:

g(x) = 2(x + 4)(x - 7)

So, the correct factored form presented in the options is:

A) g(x) = 2(x + 4)(x - 7)