# How do you factor 5x^2-16x+12?

Jun 27, 2015

5x^2-16x+12 = (5x-6)((x-2)

#### Explanation:

Hoping for rational factors, we note that
the only factors of $5$ are $\left(1 , 5\right)$

So we are looking for values $a$ and $b$
$\textcolor{w h i t e}{\text{XXXX}}$$\left(1 x - a\right) \left(5 x - b\right) = 5 {x}^{2} - \left(5 a + b\right) x + a b$
such that $a \cdot b = 12$
and $5 a + b = 16$

The $\left(a , b\right)$ factors of 12 are $\left(1 , 12\right) , \left(2 , 6\right) , \left(3 , 4\right) , \left(4 , 3\right) , \left(6 , 2\right) , \left(12 , 1\right)$

We can check each pair for a pair that satisfies $5 a + b = 16$
until we find $\left(a , b\right) = \left(2 , 6\right)$
which implies our factors are
$\textcolor{w h i t e}{\text{XXXX}}$$\left(x - 2\right) \left(5 x - 6\right)$