# How do you factor the expression x^2-10x+24?

Dec 8, 2015

$\left(x - 6\right) \left(x - 4\right)$

#### Explanation:

We attempt to generate factors in the form:
$\textcolor{w h i t e}{\text{XXX}} \left(x + a\right) \left(x + b\right)$

Since the constant term: $+ 24$ is positive
we know that $a$ and $b$ have the same sign.

Since the middle term: $\left(- 10 x\right)$ is negative
we know that $a$ and $b$ are negative.

All that remains is to find factors of $24$
that add up to $10$

Factors of $24$
$\textcolor{w h i t e}{\text{XXX}} \left\{\begin{matrix}1 & 24 \\ 2 & 12 \\ 3 & 8 \\ 4 & 6\end{matrix}\right\}$

Only the factors $\left(4 , 6\right)$ add up to $10$