Question

If f, of, x, equals, 4, x, cubed, minus, 3, x, squared, minus, 1f(x)=4x
3
−3x
2
−1, then what is the remainder when f, of, xf(x) is divided by x, minus, 1x−1?

Answer 1

Remainder = f(xf(x)) evaluated at x = 1. f(1) = 4(1)^3 − 3(1)^2 − 1 = 0, so f(1·f(1)) = f(0) = −1.

Thus the remainder is −1.