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

Question

1538 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-17T06:25:33

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

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

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 $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_1*N_2 = a*c = 1*2 = 2$
and
$N_1 +N_2 = b = 3$

After trying out a few numbers we get $N_1 = 2$ and $N_2 =1$
$2*1 = 2$ , and $2+(1)=3$

$x^2+3x+2 =x^2+2x+1x+2$
$x(x+2) +1(x+2)=0$
$(x+1)(x+2) =0$

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

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