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## Homework Statement

Let {p, q} be linearly independent polynomials. Show that {p, q, pq} is linearly independent if and only if deg p ≥ 1 and deg q ≥ 1.

## Homework Equations

λ

_{1}p + λ

_{2}q = 0 ⇔ λ

_{1}= λ

_{2}= 0

## The Attempt at a Solution

λ

_{1}p + λ

_{2}q + λ

_{3}pq = 0

I know if λ

_{3}= 0, then the coefficients of and q must be zero, but if λ

_{3}≠ 0, how do I show the degrees must be greater than or equal to 1?