# How do you factor 3x^2 + 28x + 32?

Sep 27, 2016

$\left(3 x + 4\right) \left(x + 8\right)$

#### Explanation:

$3 {x}^{2} + 28 x + 32$

Find factors of 32 which ADD to make 28.
The signs are the same both positive

As 3 isa prime number, its only factors are 3 and 1.

As a start, ask what factors of 32 can we use to get to just less than 28. (we still have to ADD on something...)

$3 \times 8 = 24$ seems a possible start.
Choose factors and cross-mulitply

$\textcolor{w h i t e}{\times x} 3 \textcolor{w h i t e}{\times x} 32$

$\textcolor{w h i t e}{\times x} 3 \textcolor{w h i t e}{\times \times} 4 \text{ } \rightarrow 1 \times 4 = 4$
$\textcolor{w h i t e}{\times x} 1 \textcolor{w h i t e}{\times \times} 8 \text{ } \rightarrow 3 \times 8 = \underline{24}$
$\textcolor{w h i t e}{\times \times \times \times \times \times \times \times \times \times} 28$

$\left(3 x + 4\right) \left(x + 8\right)$