Suppose p and q are two polynomials in Zx and degp n degq

Suppose p and q are two polynomials in Z[x] and deg(p) = n, deg(q) = m.

What can you say about deg(pq)?

deg(pq) must be equal to n + m

deg(pq) could be less than n + m, it depends on the specific p and q.

deg(pq) = max{n, m}

deg(pq) = nm

Solution

Given, deg(p) = n, hence say p = a_n xⁿ + a_n-1x^n-1+...+a₀

Given, deg(q) = m, hence say q = b_mx^m + b_m-1x^m-1+...+b₀

_{So, pq = (}a_n xⁿ + a_n-1x^n-1+...+a_0)*(b_mx^m + b_m-1x^m-1+...+b₀₎

   ₌ a_nb_mx^m+n + .... + a₀b₀

_{So, we can see, deg(pq) = m+n.}

_{Option (a)}