Question

question
factor.
$x^2 - 3x - 40$

Explanation:

Step1: Find pair of factors of -40

We need two numbers that multiply to $-40$ and add to $-3$. These numbers are $-8$ and $5$, since $(-8) \times 5 = -40$ and $(-8) + 5 = -3$.

Step2: Split middle term and factor

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

$$\begin{align*} x^2 - 3x - 40 &= x^2 - 8x + 5x - 40 \\ &= x(x - 8) + 5(x - 8) \\ &= (x - 8)(x + 5) \end{align*}$$

Answer:

$(x - 8)(x + 5)$