Question

what value of $g$ makes the equation true?
$(x+7)(x-4)=x^{2}+gx-28$
$\bigcirc -11$
$\bigcirc -3$
$\bigcirc 3$
$\bigcirc 11$

Explanation:

Step1: Expand left-hand side

Use distributive property (FOIL):
$$(x+7)(x-4) = x^2 -4x +7x -28$$

Step2: Combine like terms

Simplify the linear terms:
$$x^2 + (-4+7)x -28 = x^2 +3x -28$$

Step3: Match coefficients

Compare to $x^2 +gx -28$, so $g=3$.

Answer:

C. 3