Provide an appropriate response.
-What is the minimum number of x intercepts that a polynomial of degree 8 can have? Explain.
A) 0 because a polynomial of even degree may not cross the x axis at all.
B) 8 because this is the degree of the polynomial.
C) 1 because a polynomial of even degree crosses the x axis at least once.
D) Not enough information is given.

Question

Quizplus · Accepted Answer

A polynomial of degree 8 may have zero x intercepts if it does not cross the x axis. An even degree polynomial may not cross the x axis at all, as the end behavior will be the same on both sides of the y-axis. A polynomial of even degree may not cross the x axis at all. Therefore, the minimum number of x intercepts that a polynomial of degree 8 can have is 0.

Provide an Appropriate Response