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

1 Answer
EZ as pi
Sep 28, 2016

The remainder = 0, which means that #(p-2)# is a factor of the expression.

Explanation:

Let #f(p) = p^4-8p^3+10p^2+2p+4#

If #p-2 = 0 " "rarr p = 2#

Find #f(2)# which will give the remainder.

#f(2) = 2^4-8(2)^3+10(2)^2+2(2)+4#

#f(2) = 16-64+40+4+4 =0#

The remainder = 0, which means that #(p-2)# is a factor of the expression.

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