Question

Whst is the remainder when f(x)=x^3+3x^2-10x-4 is diveded by x-3

Answer 1

The polynomial remainder theorem allows us to calculate the remainder when a polynomial is divided by a linear polynomial:
The remainder of f(x) divided by (x-k) equals f(k).

Thus
f(x)=x^3+3x^2-10x-4 divided by x-3
gives a remainder of
f(3)=27+3(9)-10(3)-4=27+27-30-4=20
Therefore the remainder required is 20.