How do you use the factor theorem to determine whether x-2 is a factor of #x^3 + 2x^2 - 5x - 6#?

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Answer 1 · 2016-09-08T02:23:13

#(x-2)# is a factor of #x^3+2x^2-5x-6#.

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

Hence to determine whether #(x-2)# is a factor of #x^3+2x^2-5x-6# or not, one needs to find the value of #f(2)#.

As #f(x)=x^3+2x^2-5x-6#,

#f(2)=2^3+2×2^2-5×2-6#

= #8+8-10-6#

=#0#

Hence, #(x-2)# is a factor of #x^3+2x^2-5x-6#.