Question

A polynomial of degree 3 is multiplied by a polynomial of degree 5. What is the degree of the product?

Answer 1

8

Explanation:

The degree of a polynomial refers to the term with the highest exponent. Thus the highest exponent in a degree 3 polynomial is x3; for a degree 5 polynomial, it's x5. When you multiply

x3*x5 = x3+5 = x8.

So the product of a degree 3 polynomial and a degree 5 polynomial is a degree 8 polynomial.

Your leading term will result from the 3-degree term of the first polynomial, and the 5-degree term of the second. So you'll have something like ax3 * bx5. That will result in x3*x5=x8, so your product will have degree 8.