# How do you solve x^2+3x+2=0 by factoring?

Aug 17, 2015

The solutions are
color(blue)(x=-1
color(blue)(x=-2

#### Explanation:

${x}^{2} + 3 x + 2 = 0$

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

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:

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

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

${x}^{2} + 3 x + 2 = {x}^{2} + 2 x + 1 x + 2$
$x \left(x + 2\right) + 1 \left(x + 2\right) = 0$
$\left(x + 1\right) \left(x + 2\right) = 0$

Now we equate the factors to zero.
x+1=0, color(blue)(x=-1
x+2=0, color(blue)(x=-2