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

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Answer 1 · 2015-09-29T12:56:07

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

# color(blue)(x=-2#

#x^2+3x+2#

We can Split the Middle Term of this expression to factorise it.

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 = 1# and #N_2 =2#

#1*2 = 2#, and #1 +2 =3#

#x^2+3x+2 =x^2+2x+1x+2#

#=x(x+2)+1(x+2)#

#=(x+1)(x+2)#

Now we equate the factors to zero to obtain the solutions
#x+1=0, color(blue)(x=-1#

#x+2=0, color(blue)(x=-2#