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1. The problem statement, all variables and given/known data

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.

3. The attempt at a solution

I am pretty sure the statement to prove is incorrect.

If we use deg(p) = -1 and deg(q) = -2, we can easily show that the two are linearly independent (consider the functions p(x) = 1/x and q(x) = 1/x^2).

We can have k/x + l/x^2 = 0

then kx + l = 0.

Then we can differentiate and get k = 0 and l = 0, which disproves the statement.

How does this make any sense?

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# Linear independence?

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