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

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.