Question

Factorise:x² ​- x - 72

Answer 1

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like ax2+bx+c, we need to think of 2 numbers such that:

N1⋅N2=a⋅c=1⋅(−72)=−72

AND

N1+N2=b=−1

After trying out a few numbers we get N1=−9 and N2=8

8⋅(−9)=−72, and 8+(−9)=−1

x2−x−72=x2−9x+8x−72

=x(x−9)+8(x−9)

(x−9) is a common factor to each of the terms

=(x+8)(x−9)

(x+8)(x−9) is the factorised form of the expression.