Question

Two polynomial functions are given. Is the degree of the quotient of m(x) and p(x) less than, greater than, or equal to the degree of p(x)? Will this always be true when dividing polynomial functions?

A. Less than
B. Greater than
C. Equal to
D. Depends on specific polynomials

Answer 1

The degree of the quotient of two polynomial functions can be less than, greater than, or equal to the degree of the divisor polynomial, depending on the specific polynomials.

Step-by-step explanation:

The degree of the quotient of two polynomial functions is equal to the difference in degree between the dividend and divisor functions. So, in this case, if the degree of p(x) is n and the degree of m(x) is m, then the degree of the quotient m(x) / p(x) will be m - n.

This means that the degree of the quotient can be less than, greater than, or equal to the degree of p(x), depending on the specific polynomials m(x) and p(x). Therefore, the answer to whether the degree of the quotient is less than, greater than, or equal to the degree of p(x) is option D: Depends on specific polynomials.

It is important to note that this is not always true when dividing polynomial functions. The degree of the quotient can vary depending on the specific polynomials being divided.