How do you solve #x^2 - x - 12 = 0# by factoring?

1 Answer
Aug 16, 2015

Answer:

The solutions are
# color(blue)(x=-3#
#color(blue)(x=4#

Explanation:

#x^2−x−12=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*-12 = -12#
AND
#N_1 +N_2 = b = -1#

After trying out a few numbers we get #N_1 = 3# and #N_2 =-4#
#3*-4 = -12#, and #3+(-4)= -1#

#x^2−x−12=x^2−4x+3x−12#

#x(x-4) +3(x−4)=0#

#(x+3)(x-4)=0#

Now we equate the factors to zero.
#x+3 = 0 , color(blue)(x=-3#
#x-4 = 0 , color(blue)(x=4#