Finding Polynomials in the Kernel of the Evaluation Homomorphism θ_5

[SMA_01]

Homework Statement

For the evaluation homomorphism θ_5: Q[x]→ℝ, find 6 elements in the kernel of the homomorphism.

The Attempt at a Solution

Basically, I find 6 polynomials with rational coefficients that will equal zero when evaluated at 5, am I correct on this?

So far I have 0, x-5, x^2-25. Is x^3-5x^2-25x+125 one also?

Thanks

 

[hamsterman]

Yes to both.