How do you find the remainder when #f(x)=5x^6-3x^3+8; x+1#?

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Answer 1 · 2016-05-07T15:59:01

The remainder theorem states that whenever polynomial function #f(x)# is divided by #x - a# the remainder is given by evaluating #f(a)#

#x + 1 = 0#
#x = -1#

You will evaluate #f(-1)#

#f(-1) = 5(-1)^6 - 3(-1)^3 + 8#

#f(-1) = 5(1) - 3(-1) + 8#

#f(-1) = 5 + 3 + 8#

#f(-1) = 16#

Hence, the remainder will be 16.

Hopefully this helps!