Question

which expression is a factor of $x^2 + 7x - 30$?\
\bigcirc $x + 15$\
\bigcirc $x - 10$\
\bigcirc $x + 5$\
\bigcirc $x - 3$

Explanation:

Step1: Find pair for factoring

Find two numbers that multiply to $-30$ and add to $7$. The numbers are $10$ and $-3$.

Step2: Factor the quadratic

Rewrite and factor by grouping:

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

Step3: Match with options

Compare the factors to the given choices.

Answer:

D. x-3