Question

complete the equation to show two equivalent expressions.\\(g^2 - 4g - 21 = (g - square)(g + square)\\)

Explanation:

Step1: Find factors of -21

We need two numbers that multiply to $-21$ and add to $-4$. These numbers are $-7$ and $3$, since $(-7) \times 3 = -21$ and $(-7) + 3 = -4$.

Step2: Factor the quadratic

Substitute the numbers into the factored form of the quadratic.
$g^2 - 4g - 21 = (g - 7)(g + 3)$

Answer:

The first blank is 7, the second blank is 3. The completed equation is $g^2 - 4g - 21 = (g - 7)(g + 3)$