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

Aug 11, 2015

color(blue)((2x-1)(x+3) is the factorised form of the expression.

#### Explanation:

2x^2+5x−3
We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 2 \cdot \left(- 3\right) = - 6$
and
${N}_{1} + {N}_{2} = b = 5$

After trying out a few numbers we get ${N}_{1} = 6$ and ${N}_{2} = - 1$

$6 \cdot \left(- 1\right) = - 6$, and $6 + \left(- 1\right) = 5$

2x^2+color(blue)(5x)−3 = 2x^2+color(blue)(6x -1x)−3

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

color(blue)((2x-1)(x+3) is the factorised form of the expression.