- #1

Terrell

- 317

- 26

## Homework Statement

find the number of polynomials f(x) that satisfies the condition:

f(x) is monic polynomial, has degree 1000, has integer coefficients, and it can divide f(2x^3 + x)

i would very much prefer that you guys give me hints first. thanks

## Homework Equations

remainder factor theorem

## The Attempt at a Solution

since f(2x^3 + x) = q(x)*f(x) such that q(x) is of degree 2000 and f(x) is of degree 1000 because f(2x^3 + x) is of degree 3000.

since the problem asked for the number of f(x) that satisfies the condition, then i think it would be the number of ways to choose 1000 first degree polynomials in a group of 3000 first degree polynomials, which i think would be 3000C1000...? but wolfram alpha tells me the number has 829 digits which i think must be wrong because it doesn't fit the answer box that I'm trying to input my answer into.