# Factor each polynomial?

## $2 {x}^{2} + 5 x + 2$ I missed a week of school and my teacher will not re-teach so please help.

May 26, 2018

$\rightarrow 2 {x}^{2} + 5 x + 2 = \left(x + 2\right) \left(2 x + 1\right)$

#### Explanation:

$\rightarrow 2 {x}^{2} + 5 x + 2$

$= 2 {x}^{2} + 4 x + x + 2$

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

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

May 26, 2018

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

#### Explanation:

$\text{given a quadratic in "color(blue)"standard form}$

•color(white)(x)ax^2+bx+c color(white)(x);a!=0

$\text{to factor consider the factors of the product ac which}$
$\text{sum to b}$

$2 {x}^{2} + 5 x + 2 \text{ is in standard form}$

$\text{with "a=2,b=5" and } c = 2$

$\text{consider the factors of the product } 2 \times 2 = 4$
$\text{which sum to + 5}$

$\text{the factors required are + 4 and + 1}$

$\text{split the middle term using these factors}$

$2 {x}^{2} + 4 x + x + 2 \leftarrow \textcolor{b l u e}{\text{factor by grouping}}$

$= \textcolor{red}{2 x} \left(x + 2\right) \textcolor{red}{+ 1} \left(x + 2\right)$

$\text{take out the "color(blue)"common factor } \left(x + 2\right)$

$= \left(x + 2\right) \left(\textcolor{red}{2 x + 1}\right)$

$2 {x}^{2} + 5 x + 2 = \left(x + 2\right) \left(2 x + 1\right)$