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,

$\mathrm{<i>P(x)\; =\; ax^p + \; ...\; + \; bx^q</i>}$
$\mathrm{<i>Q(x)\; =\; cx^r + \; ...\; + \; dx^s</i>}$

Where . . .

• $$ a , b , c , d ≠ 0
• $\mathrm{<i>p</i>}>\mathrm{<i>q</i>}\ge \; <i>0</i>\mathrm{}$ and $$ r > s ≥ 0
• $$ p + r > q + s
• Of course, the terms omitted between have intermediate degree.

Then, the product $\mathrm{<span>P.Q</span>}$ has at least two terms acx^p+r and bdx^q+s where ac and bd are not zero.