Select the correct answer. Which equation shows function g in factored form? g(x)=2x^2-6x-56 g(x)=2(x2-3x-28) g(x)=(2x+7)(x-8) g(x)=2(x-4)(x+7) g(x)=2(x+4)(x-7)

To find the correct equation that shows function g in factored form, we need to factorize the given equation $g(x)=2x^{2}-6x-56$.<br /><br />Step 1: Factor out the common factor of 2 from the equation:<br />$g(x) = 2(x^{2}-3x-28)$<br /><br />Step 2: Factorize the quadratic expression inside the parentheses:<br />We need to find two numbers whose product is -28 and whose sum is -3. These numbers are -7 and 4.<br /><br />Step 3: Rewrite the quadratic expression using the factors found:<br />$x^{2}-3x-28 = (x-7)(x+4)$<br /><br />Step 4: Substitute the factored form back into the equation:<br />$g(x) = 2(x-7)(x+4)$<br /><br />Therefore, the correct answer is:<br />$g(x)=2(x-7)(x+4)$