How do you use the remainder theorem to see if the #x+6# is a factor of #x^5+6x^4-3x^2-22x-29#?

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Answer 1 · 2017-02-17T10:33:46

See explanation.

According to the Reminder theorem to see if #(x-a)# is a factor of a polynomial #P(x)# you have to check if #P(a)=0#

In the given example we have:

#P(x)=x^5+6x^4-3x^2-22x-29# and #a=-6#, so:

#P(-6)=(-6)^5+6*(-6)^4-3*(-6)^2-22*(-6)-29#

#=-7776+7776-108+132-29=132-108-29=#

#=24-29=-5#

The value #P(-6)# is different from zero, so the polynomial is not divisible by #(x+6)#