Question

which shows the factored form of $x^2 - 12x - 45$?
$\bigcirc$ $(x + 3)(x - 15)$
$\bigcirc$ $(x - 3)(x - 15)$
$\bigcirc$ $(x + 3)(x + 15)$
$\bigcirc$ $(x - 3)(x + 15)$

Explanation:

Step1: Identify target factors

We need two numbers that multiply to $-45$ and add to $-12$. These numbers are $3$ and $-15$, since $3\times(-15)=-45$ and $3+(-15)=-12$.

Step2: Write factored form

Substitute the numbers into the binomial form $(x+a)(x+b)$, where $a=3$ and $b=-15$.
<Expression>$(x + 3)(x - 15)$</Expression>

Step3: Verify by expanding

Use the FOIL method to check:

$$\begin{align*} (x + 3)(x - 15)&=x^2-15x+3x-45\\ &=x^2-12x-45 \end{align*}$$

This matches the original quadratic.

Answer:

A. $(x + 3)(x - 15)$