How do you use the remainder theorem to find the remainder for the division #(x^4+5x^3-14x^2)div(x-2)#?

1 Answer
EZ as pi
Sep 8, 2016

#f(2) = 0# There is no remainder.
#x-2# is a factor.

Explanation:

If we have #f(x) = x^4 +5x^3-14x^2#

Let #x-2 = 0 rarr x =2#

The remainder of #x^4 +5x^3-14x^2 div(x-2)#
is found from #f(2)#

#f(2) = 2^4 +5(2)^3-14(2)^2#

=# 16+40-56 =0#

The fact that the remainder is 0, (ie there is no remainder), means that #(x-2)# is a factor of #x^4 +5x^3-14x^2#

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