How do you factor #2v^2 + 11v + 5#?

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Answer 1 · 2015-05-30T17:55:06

#2v^2+11v+5#

#= 2v^2+v+10v+5#

#=(2v^2+v)+(10v+5)#

#=v(2v+1)+5(2v+1)#

#=(v+5)(2v+1)#

How did I know to split the middle term into #v + 10v#?

I used a variant of the AC Method:

#A=2#, #B=11#, #C=5# are the coefficients of the quadratic.

Look for a pair of factors of #AC=10# whose sum is #B=11#.

#1 xx 10 = 10# and #1 + 10 = 11#