Question

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

Answer 1

The degree of the quotient of m(x) and p(x) is less than the degree of p(x). This is not always true when dividing polynomial functions.

Step-by-step explanation:

The degree of a polynomial function is determined by the highest power of x in the function. In this case, the polynomial function p(x) = x^2 - 4 has a degree of 2 because the highest power of x is 2. The polynomial function m(x) = 2x^3 + x - 16 has a degree of 3 because the highest power of x is 3.

To find the quotient of m(x) divided by p(x), we divide the leading term of m(x) by the leading term of p(x), which gives us 2x. The quotient has a degree one less than the difference in degrees of the two polynomials. Therefore, the degree of the quotient is equal to 3 - 2 = 1, which is less than the degree of p(x).

This is not always true when dividing polynomial functions. The degree of the quotient can be less than, equal to, or greater than the degree of the divisor depending on the specific polynomials being divided.