Question

factor. $x^{2}-2x-15$

Explanation:

Step1: Find pair with product -15, sum -2

We need two numbers that multiply to $-15$ and add to $-2$. These numbers are $-5$ and $3$, since $(-5)\times3=-15$ and $(-5)+3=-2$.

Step2: Split middle term and factor

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

$$\begin{align*} x^2 - 2x - 15&=x^2 -5x +3x -15\\ &=x(x-5)+3(x-5)\\ &=(x-5)(x+3) \end{align*}$$

Answer:

$(x-5)(x+3)$