# How do you factor 3h^2 + 19h + 20?

Jun 2, 2015

$f \left(h\right) = 3 {h}^{2} + 19 h + 20$

Let's use AC Method, with a twist...

$A = 3$, $B = 19$, $C = 20$

Look for a factorization of $A C = 3 \cdot 20 = 60$ into a pair of factors whose sum is $B = 19$.

The pair $B 1 = 4$, $B 2 = 15$ works.

Then for each of the combinations $A$, $B 1$ and $A$, $B 2$, divide by the $\text{HCF}$ (highest common factor) to get the coefficients of a factor of $f \left(h\right)$...

$\left(A , B 1\right) = \left(3 , 4\right)$ $\left(\text{HCF 1}\right)$$\rightarrow$$\left(3 , 4\right)$$\rightarrow$$\left(3 h + 4\right)$
$\left(A , B 2\right) = \left(3 , 15\right)$ $\left(\text{HCF 3}\right)$$\rightarrow$$\left(1 , 5\right)$$\rightarrow$$\left(h + 5\right)$

So $f \left(h\right) = 3 {h}^{2} + 19 h + 20 = \left(3 h + 4\right) \left(h + 5\right)$