# How do you factor 10x^2+3x-4?

Aug 10, 2015

color(blue)((2x-1)( 5x +4) is the factorised form of the expression.

#### Explanation:

10x^2+3x−4

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 10 \cdot - 4 = - 40$
and,
${N}_{1} + {N}_{2} = b = 3$

After trying out a few numbers we get ${N}_{1} = 8$ and ${N}_{2} = - 5$
$8 \cdot - 5 = - 40$, and $8 + \left(- 5\right) = 3$

10x^2+color(blue)(3x)−4 = 10x^2+color(blue)(8x - 5x)−4

=2x( 5x +4)−1(5x+4)

color(blue)((2x-1)( 5x +4) is the factorised form of the expression.