Question

Two polynomial functions are given.m(x)=2x3+x−16p(x)=x2−4

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. It depends on the specific functions.

Answer 1

The degree of the quotient of m(x) and p(x) is less than the degree of p(x). This is generally true when dividing polynomial functions.

Step-by-step explanation:

The degree of a polynomial function is the highest power of the variable in the function. In this case, the degree of m(x) is 3 and the degree of p(x) is 2. When we divide m(x) by p(x), the degree of the quotient will be the difference between the degrees of m(x) and p(x). So, the degree of the quotient of m(x) and p(x) will be 1 (3 - 2). This means that the degree of the quotient is less than the degree of p(x).

When dividing polynomial functions, the degree of the quotient depends on the degrees of the dividend and the divisor. If the degree of the dividend is greater than or equal to the degree of the divisor, then the degree of the quotient will be less than or equal to the degree of the dividend. If the degree of the dividend is less than the degree of the divisor, then the degree of the quotient will be less than the degree of the divisor.