Can the Product of Two Polynomials Result in a Single Term? | SJB -->

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### Can the Product of Two Polynomials Result in a Single Term?

By assuming that we are talking about polynomials with real coefficients. Suppose that the polynomials are,

Where . . .
•  a , b , c , d 0
• $p>q\ge 0$ and  r > s ≥ 0
•  p + r > q + s
• Of course, the terms omitted between have intermediate degree.
Then, the product $\mathrm{P.Q}$ has at least two terms acxp+r and bdxq+s where ac and bd are not zero.

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