Question

factor each expression
g² - 89g - 48

Explanation:

Step1: Identify $a,b,c$ for $ax^2+bx+c$

For $g^2-8g-48$, $a=1$, $b=-8$, $c=-48$

Step2: Find two factors of $ac$ summing to $b$

$ac=1\times(-48)=-48$. The pair $4$ and $-12$ satisfies $4+(-12)=-8=b$.

Step3: Split middle term and factor by grouping

$$\begin{align*} g^2-8g-48&=g^2+4g-12g-48\\ &=g(g+4)-12(g+4)\\ &=(g+4)(g-12) \end{align*}$$

Answer:

$(g+4)(g-12)$