Is x+4 a factor of #2x^3+3x^2-29x-60#?

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Answer 1 · 2016-09-19T08:16:23

#(x+4)# is not a factor of #f(x)=2x^3+3x^2-29x-60#

According to factor theorem if #(x-a)# is a factor of polynomial #f(x)#, then #f(a)=0#.

Here we have to test for #(x+4)# i.e. #(x-(-4))#. Therefore, if #f(-4)=0# then #(x+4)# is a factor of #f(x)=2x^3+3x^2-29x-60#.

#f(-4)=2(-4)^3+3(-4)^2-29(-4)-60#

= #2×(-64)+3×16-29×(-4)-60#

= #-128+48+116-60#

= #164-188=-24#

Hence #(x+4)# is not a factor of #f(x)=2x^3+3x^2-29x-60#.