Question

factor:
$x^2 + 7x - 30$
$(x + 10)(x - 3)$
$(x + 10)(x - 7)$
$(x - 10)(x + 3)$
$(x + 10)(x + 3)$

Explanation:

Step1: Find pair for sum 7, product -30

We need two numbers that add to $7$ and multiply to $-30$. The numbers are $10$ and $-3$, since $10 + (-3) = 7$ and $10 \times (-3) = -30$.

Step2: Split middle term and factor

Rewrite the quadratic: $x^2 + 10x - 3x - 30$
Group and factor: $x(x+10) - 3(x+10) = (x+10)(x-3)$

Step3: Verify with expansion

Expand $(x+10)(x-3)$:

$$\begin{align*} (x+10)(x-3) &= x^2 - 3x + 10x - 30\\ &= x^2 +7x -30 \end{align*}$$

This matches the original quadratic.

Answer:

A. $(x + 10)(x - 3)$