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

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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#