Question

factor.
$w^2 - 24w + 23$

Explanation:

Step1: Find pair of factors for 23

We need two numbers that multiply to $23$ and add to $-24$. These numbers are $-1$ and $-23$, since $(-1)\times(-23)=23$ and $(-1)+(-23)=-24$.

Step2: Split middle term and factor

Rewrite the quadratic using the pair, then factor by grouping:

$$\begin{align*} w^2 -24w +23&=w^2 -w -23w +23\\ &=w(w-1)-23(w-1)\\ &=(w-1)(w-23) \end{align*}$$

Answer:

$(w-1)(w-23)$