Question

What is the remainder when x^4 + 7 is divided by x - 3

Answer 1

Let f(x)=x

4

+4x

3

−5x

2

−6x+7.

Let R be the remainder obtained when f(x) is divided by x+3.

Equate x+3 to 0 and put the value of x in f(x).

x+3=0

⟹x=−3

R=(−3)

4

+4(−3)

3

−5(−3)

2

−6(−3)+7

=81−108−45+18+7

=−47

Thus required remainder is −47