Chapter 8.3, Problem 7LC

To determine

To find: The relation between degrees of two polynomials and degree of their product.

Answer to Problem 7LC

Degree of polynomial obtained as a product of two polynomials is the sum of degrees of both the polynomials.

Explanation of Solution

Given information: Any two polynomials $p(x)$ and $q(x)$ are given that to be multiplied.

Concept used: The degree of a polynomial is the highest power on its any of the term. And when two such polynomials are multiplied together, the degree of the resulting polynomial is always the sum of degrees of both the polynomials.

Calculation: For example, let $p(x)=x^3$ and $q(x)=x^2$ be two polynomials so that degree of first polynomial is 3 and of second is 2. So, $p(x)\times q(x)=x^5$ .

Or degree of resulting product of 5 that is the sum of degrees of both the polynomials.

Conclusion: So, degree of product of two polynomials is the sum of degrees of two polynomials.