The Remainder Theorem?

Question

1. x3 - 2x2 + 5x - 6 divided by x - 3


2. -2x4 - 6x2 + 3x + 1 divided by x + 1

3. x5 + 2x4 - 3x + 3 divided by x - 1

4. Find a polynomial of degree three that when divided by x - 2 has a remainder of 3. You will really have to think on this one. Hint: Work backwards!

Answer 1

the remainder theorem says if the p(x) is divided by x-c
then the remainder is p(c)

so 1, 3^3 - 2*3^2 + 5*3 - 6 = 18

so try p(-1) and p(1) for 2 and 3.

Answer 2

first three you can do by putting (x -- 3) = 0, (x + 1) = 0, (x -- 1) = 0 see the
4. polynomial is
f(x -- 2) + 3 . where f(y) = ay^n + by^(n--1) + cy^(n--2) + ..... + y