Question

Which of the following statement is not always true

A. The leading coefficient and the degree are the only determining factors in the end behavior of the polynomial function.

B. A function is odd if every X in the denominator -F(x) equals F (-x)therefore every odd degree polynomial function is also an odd function

C.If f(x)and g(x) are polynomials then the products is a polynomial

D. a polynomial function with an arctic must have at least one real zero

Answer 1

If you multiply the polynomials (x - 1) and (x + 1), you get the function x^2 - 1 which is not a polynomial. The statement that is not always true is option C: If f(x) and g(x) are polynomials, then the product is a polynomial.

Step-by-step explanation:

The statement that is not always true is option C: If f(x) and g(x) are polynomials, then the product is a polynomial.

This statement is not always true because the product of two polynomials may result in a non-polynomial function. For example, if you multiply the polynomials (x - 1) and (x + 1), you get the function x^2 - 1 which is not a polynomial.

Therefore, option C is the correct answer.