How do you factor d^2 + 8d +7?

1 Answer
May 20, 2016

color(green)( (d + 1) ( d + 7 ) is the factorised form of the expression.

Explanation:

d^2 + 8d + 7

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

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

N_1*N_2 = a*c = 1* 7 = 7

AND

N_1 +N_2 = b = 8

After trying out a few numbers we get N_1 = 7 and N_2 =1
7*1 = 7, and 7 + 1 = 8

d^2 + color(green)(8d) + 7 = d^2 + color(green)((7d + 1d)) + 7

= d ( d + 7 ) + 1 ( d + 7 )

(d+7) is a common factor to each of the terms

=color(green)( (d + 1) ( d + 7 )