Question

what is the remainder when f(x)=-9x^17+x^13-x^2+8x is divided by x+1?

Answer 1

f(-1) = -9(-1)^17+(-1)^13-(-1)^2+8(-1) = 9-1-1-8=-1
by remainder theorem,
the remainder is -1

Answer 2

We have
\[ f(x)=-9x^{17}+x^{13}-x^2+8x\]
We have to divide it by x+1
Use remainder theorem here
put x=-1 in f(x)
which will give us the remainder
\[f(-1)=-9(-1)^{17}+(-1)^{-13} -(-1)^2+8(-1)=-9 \times -1+ (-1) -(1)-8\]
we get
\[f(-1)=9-1-1-8=-1\]
so the remainder is -1

Answer 3

oh ok thank you