# How do you factor completely: 3x^2 + 2x − 1?

Jul 24, 2015

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

#### Explanation:

3x^2+2x−1

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:

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

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

3x^2+2x−1 =3x^2+3x -1x−1

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

$\left(x + 1\right)$is common to both terms here:

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