# How do you factor completely: 8x^2 − 11x + 3?

Jul 17, 2015

 = color(blue)((8x-3)(x-1)

#### Explanation:

8x^2−11x+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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 8 \cdot 3 = 24$
and
${N}_{1} + {N}_{2} = b = - 11$

After trying out a few numbers we get:
${N}_{1} = - 3$ and ${N}_{2} = - 8$

$\left(- 3\right) \cdot \left(- 8\right) = 24$ and
$\left(- 3\right) + \left(- 8\right) = - 11$

8x^2−11x+3 = 8x^2−8x - 3x+3

$8 x \left(x - 1\right) - 3 \left(x - 1\right)$

 = color(blue)((8x-3)(x-1)