Review of Polynomial Functions

Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression. It determines the polynomial's end behavior and the maximum number of real roots.

Front

How many real zeros can a polynomial function have?

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A polynomial function of degree n can have at most n real zeros.

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What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. It is determined by the leading term of the polynomial.

Front

What is multiplicity in polynomial functions?

Back

Multiplicity refers to the number of times a particular root (zero) appears in a polynomial. A root with even multiplicity touches the x-axis, while a root with odd multiplicity crosses the x-axis.

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Back

The multiplicity of the zero x=1 is 4.

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Back

The root x=1 has even multiplicity.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It influences the direction of the polynomial's end behavior.

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What is the difference between even and odd degree polynomials?

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Even degree polynomials have the same end behavior on both sides (both up or both down), while odd degree polynomials have opposite end behavior (one side up and the other down).

Front

How do you determine the number of turning points in a polynomial function?

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The maximum number of turning points of a polynomial function is n-1, where n is the degree of the polynomial.