How do you find the remainder (without division) when 4x^3 - 3x^2 + 2x - 4 is divisible by x + 2?

Answer 1

You mean "divided by" not "divisible by"!

Let f(x) represent the cubic polynomial in the problem.

f(x) = Q(x)(x+2) + R(x)

Consequently f(-2) = 0 + R(-2).

This tells you that the remainder is f(-2)