How do you factor completely: #x^2 − 3x − 28#?

1 Answer
Jul 13, 2015

Answer:

#=color(blue)((x+4)(x-7)#

Explanation:

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*-28 = -28#
and
#N_1 +N_2 = b = -3#

After trying out a few numbers we get #N_1 = -7# and #N_2 =4#
#7*-4 = -28#, and #4+(-7)= -3#

#x^2 -3x -28#
#=x^2 -7x +4x -28#
#=x(x-7)+ 4(x -7)#

#=color(blue)((x+4)(x-7)#