Given that the polynomial f(x) has degree 8, which of the following most accurately describes the number of turning points of f(x)?

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The x intercepts are the roots of the polynomial f(x) = 0.
The fundamental theorem of algebra says that the number of roots of this equation is 9, but not necessarily all of them are real; therefore the MAXIMUM number of x intercepts is 9.
However, since f(x) is of odd degree it must have at least one real root; therefore, the MINIMUM number of x intercepts is 1.

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ap8997154 ap8997154 · Answer 2 · 2022-07-14T09:19:07+02:00

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The polynomial f(x) that has a degree of 8 will have 7 turning points.

What is a polynomial?

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

For any polynomial equation, the number of turning points is always less than or equal to the degree of the polynomial.

Generally, the number of turns is one less than the degree of the polynomial.

Hence, the polynomial f(x) that has a degree of 8 will have 7 turning points.

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