Final answer:
An 8th degree polynomial can have a maximum of 7 turning points, which is determined by subtracting one from the degree of the polynomial. This is the maximum number of times the graph of the polynomial can change direction.
Step-by-step explanation:
The maximum number of turning points a 8th degree polynomial could have is determined by the degree of the polynomial minus one. For an 8th degree polynomial, the maximum number of turning points it could have is 7. A turning point is where a polynomial changes direction from increasing to decreasing or vice versa.
A polynomial of degree n can have up to n-1 turning points. This is because the turning points are where the first derivative of the polynomial changes sign, which indicates a change in the direction of the graph of the polynomial. Therefore, a polynomial of degree 8, which is a polynomial whose highest exponent of the variable is 8, could potentially change direction 7 times.
However, it's important to note that this is the maximum number of turning points, and an 8th degree polynomial might have fewer than 7 turning points, depending on its specific coefficients and terms.