# How do you factor the expression 2x^2+ 5x + 3?

May 2, 2016

$\left(2 x + 3\right) \left(x + 1\right)$

#### Explanation:

When you want to factorise a quadratic expression, each part conveys information. $\textcolor{red}{2} {x}^{2} \textcolor{g r e e n}{+} \textcolor{y e l l o w}{5} x \textcolor{b l u e}{+} \textcolor{red}{3}$

Match the colours to the information it conveys.

Find the factors of $\textcolor{red}{2} \mathmr{and} \textcolor{red}{3}$ which $\textcolor{b l u e}{A D D}$ together to give $\textcolor{y e l l o w}{5}$.
The signs in the brackets will be the $\textcolor{b l u e}{S A M E}$, they are both $\textcolor{g r e e n}{p o s i t i v e}$.

$2 x 3$ $\Rightarrow 1 \times 3 = 3$
$1 x 1$ $\Rightarrow 2 \times 1 = 2$ $3 + 2 = 5$

$\left(2 x + 3\right) \left(x + 1\right)$