Polynomial Functions

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8 Terms

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Polynomial Function

A function expressed in the form \( P(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0 \) with non-negative integer \( n \) and non-zero coefficient \( a_n \).

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Degree

The highest power of \( x \) with a non-zero coefficient in a polynomial function.

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Leading Coefficient

The coefficient of the term with the highest degree in a polynomial function.

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Root

A solution to the equation \( P(x) = 0 \) for a polynomial function.

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Factor Theorem

If \( c \) is a root of \( P(x) \), then \( x - c \) is a factor of \( P(x) \).

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End Behavior

Behavior of a polynomial function determined by the leading term \( a_nx^n \) for even/odd \( n \) and positive/negative \( a_n \).

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Turning Points

Points where a polynomial function changes direction, with up to \( n-1 \) turning points for a polynomial of degree \( n \).

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Intercepts

Points where a polynomial function crosses the x-axis (roots) and y-axis (constant term).