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

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- October 15th 2007, 07:45 AMoceanmdPlease help to find k and remainder
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 - October 15th 2007, 09:13 AMSoroban
Hello, oceanmd!

I believe you're expected to know the*Factor Theorem*and*Remainder Theorem.*

Quote:

Problem 1: Find such that has the factor

If is a factor of , then: .

Hence: .

. . and we have: .

Quote:

Problem 2: What is the remainder when is divided by

. .

- October 15th 2007, 09:21 AMoceanmdThank you very much
Soroban,

Thanks a lot. These problems are from the Factor Theorem and Remainder Theorem Chapter.

Have a nice rest of the day.