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

1 Answer
Sep 24, 2015

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

Explanation:

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.