How do you factor #x^2+14x-72#?

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Answer 1 · 2015-09-24T15:10:28

#color(blue)((x-4)(x+18) # is the factorised form of the expression.

#x^2 +14x -72#

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*-72 = -72#

AND

#N_1 +N_2 = b = 14#

After trying out a few numbers we get #N_1 = 18# and #N_2 =-4#

#18*-4 = -72#, and #18+(-4)= 14#

#x^2 +color(blue)(14x) -72 = x^2 +color(blue)(18x -4x )-72 #

#=x(x+18) -4(x +18) #

#color(blue)((x-4)(x+18) # is the factorised form of the expression.