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The degree of the polynomial p(x) is 11, and the degree of the polynomial q(x) is 7. Find all possible degrees of the polynomial p(x)+q(x).

 Mar 28, 2019

\(deg(p(x))\neq deg(q(x))\Rightarrow deg((p+q)(x)) = \max(deg(p(x)),deg(q(x)))\\ \text{In this case }11>7\Rightarrow deg((p+q)(x))=11\)


If the two polynomials have the same degree it's possible that terms can cancel making the resulting

degree of the sum polynomial dependent upon the individual polynomials being summed.

 Mar 28, 2019

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