How do you find the remainder when #f(x)=x^4+8x^3+12x^2; x+1#?

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Answer 1 · 2015-12-31T07:31:38

5

Simply perform long division. That is;

#(x^4+8x^3 +12x^2+0x+0)/(x+1)#

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Answer 2 · 2015-12-31T12:26:06

The remainder is #f(-1) = 5#

The remainder of dividing #f(x)# by a linear factor of the form #(x-a)# is #f(a)#.

In our case #x+1 = x - (-1)#, so evaluate #f(-1)# to find the remainder:

#f(-1) = (-1)^4+8(-1)^3+12(-1)^2 = 1-8+12 = 5#