Question

question
factor.
$x^2 - 2x - 63$

Explanation:

Step1: Find pair of factors of -63

We need two numbers that multiply to $-63$ and add to $-2$. These numbers are $-9$ and $7$, since $(-9) \times 7 = -63$ and $(-9) + 7 = -2$.

Step2: Split middle term and factor

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

$$\begin{align*} x^2 - 2x - 63 &= x^2 - 9x + 7x - 63 \\ &= x(x - 9) + 7(x - 9) \\ &= (x - 9)(x + 7) \end{align*}$$

Answer:

$(x - 9)(x + 7)$