How do you factor 2d² +d -21?

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Answer 1 · 2015-06-08T17:17:38

#2d^2 + d - 21#

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 = 2*-21 = -42#
and
#N_1 +N_2 = b = 1#

After trying out a few numbers we get #N_1 = 7# and #N_2 =-6#
#7*-6 = -42#, and #7+(-6)= 1#

#2d^2 + d - 21 = 2d^2 - 6d + 7d - 21#
#=2d(d-3)+ 7(d-3)#
#(d-3)# is common to both terms.

#=color(green)((2d+7)(d-3)#