How do you use the remainder theorem to see if the #n+2# is a factor of #n^4+10n^3+21n^2+6n-8#?

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Answer 1 · 2017-01-14T20:18:35

#n+2# is a factor of the given polynomial

The remainder theorem states that the bynomial #(x-a)# is a factor of a polynomial P(x) if P(a)=0.

Let it be

#P(n)=n^4+10n^3+21n^2+6n-8#,

then

#P(-2)=(-2)^4+10*(-2)^3+21*(-2)^2+6*(-2)-8#

#=16-80+84-12-8=0#

Then #n+2# is a factor of the given polynomial