# Math Help - Remainder Theorm

1. ## Remainder Theorm

1. Given: f(x) = x^n+y^n. for which value(s) of n is x+y a factor of f(x)

2. 2x^3-x^2-2x+2 = (2x-1).Q(x)+R(x) for all values of x. What is the value of R?

3. if x^3 + kx^2 -3 is divided by x+2 the remainder is 3 more than the remainder when the same expression is divided by x-1. find the value of k

2. Hi
Originally Posted by Yolo
1. Given: f(x) = x^n+y^n. for which value(s) of n is x+y a factor of f(x)
$x+y=x-(-y)$ is a factor of f(x) iff $-y$ is a root of $f$. When is this possible ? (consider the two cases $n$ even and $n$ odd)
2. 2x^3-x^2-2x+2 = (2x-1).Q(x)+R(x) for all values of x. What is the value of R?
What does the remainder theorem tells us about the degree of $R(x)$ ?