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

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Answer 1 · 2016-05-20T11:22:24

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

#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 ) #