Final answer:
The degree of the resulting polynomial when two polynomials are multiplied is the sum of the degrees of the original polynomials. Multiplying a quadratic by a cubic polynomial, for instance, results in a polynomial of degree 5, following the rule of adding exponents when multiplying exponential terms with the same base.
Step-by-step explanation:
When you multiply two polynomials, the degree of the resulting polynomial is the sum of the degrees of the polynomials being multiplied. For example, if you have a polynomial of degree n and another of degree m, when you multiply them, the resulting polynomial will have a degree of n+m.
To understand this, consider the general rule for multiplying exponents: when you multiply two exponential expressions with the same base, you add the exponents. Applying this rule to each term in the polynomials during multiplication, the highest degree term in the product will be the result of multiplying the highest degree terms from each polynomial together.
For instance, if you multiply a quadratic polynomial (degree 2) by a cubic polynomial (degree 3), the highest degree terms will multiply to give a term of degree 5, making the resulting polynomial of degree 5. Consequently, the degree does not simply double or increase by a fixed factor but depends on the degrees of the original polynomials.