# How do you factor y= 4x^2 + 17x + 4  ?

Sep 19, 2016

$4 {x}^{2} + 17 x + 4 = \left(4 x + 1\right) \left(x + 4\right)$

#### Explanation:

Use an AC method:

Find a pair of factors of $A C = 4 \cdot 4 = 16$ with sum $B = 17$

The pair $16 , 1$ works, so use this to split the middle term, then factor by grouping:

$4 {x}^{2} + 17 x + 4 = \left(4 {x}^{2} + 16 x\right) + \left(x + 4\right)$

$\textcolor{w h i t e}{4 {x}^{2} + 17 x + 4} = 4 x \left(x + 4\right) + 1 \left(x + 4\right)$

$\textcolor{w h i t e}{4 {x}^{2} + 17 x + 4} = \left(4 x + 1\right) \left(x + 4\right)$