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

Feb 21, 2017

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

#### Explanation:

The standard form of the $\textcolor{b l u e}{\text{quadratic function}}$ is.

$y = a {x}^{2} + b x + c$

To factorise the function.

• consider the factors of the product ac which sum to give b

$\text{for } 2 {x}^{2} + 5 x - 3$

$a = 2 , b = 5 \text{ and } c = - 3$

$\Rightarrow a c = 2 \times - 3 = - 6$

$\text{the required factors of -6 are "+6" and } - 1$

$\text{Since " 6xx-1=-6" and } + 6 - 1 = + 5$

$\text{now express " 2x^2+5x-3" as}$

$2 {x}^{2} \textcolor{red}{+ 6 x - x} - 3$

Factorise by 'grouping'

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

Take out $\textcolor{b l u e}{\text{common factor " "of }} \left(x + 3\right)$

$\Rightarrow \left(x + 3\right) \left(2 x - 1\right) \leftarrow \text{ in factorised form}$