Problem 1: Find k such that f(x)=x^4-kx^3+kx^2+1 has the factor (x+2)
Problem 2: What is the remainder when f(x)=-3x^17+x^9-X^5+2x is divided by (x+1)
Thank you
Hello, oceanmd!
I believe you're expected to know the Factor Theorem and Remainder Theorem.
Problem 1: Find such that has the factor
If is a factor of , then: .
Hence: .
. . and we have: .
When is divided by , the remainder is: .Problem 2: What is the remainder when is divided by
. .