Algebra 2 Polynomial Functions 3.1, 3.5

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What is a polynomial function?

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A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is: $$f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$$ where $a_n$ is the leading coefficient and $n$ is the degree.

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How do you classify polynomials?

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Polynomials are classified based on their degree: - Constant: Degree 0 - Linear: Degree 1 - Quadratic: Degree 2 - Cubic: Degree 3 - Quartic: Degree 4 and so on.

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What is the leading term of a polynomial?

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The leading term of a polynomial is the term with the highest degree. For example, in $$f(x) = -9x^3 + 9x^2 - 8 + 0.18x$$, the leading term is $$-9x^3$$.

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What is the leading coefficient?

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The leading coefficient is the coefficient of the leading term in a polynomial. For the polynomial $$f(x) = -9x^3 + 9x^2 - 8 + 0.18x$$, the leading coefficient is $$-9$$.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial. For example, in $$f(x) = -9x^3 + 9x^2 - 8 + 0.18x$$, the degree is 3.

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How do you write a polynomial in standard form?

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A polynomial is in standard form when its terms are arranged in descending order of degree. For example, $$f(x) = 2x^3 + 3x^2 - x + 5$$ is in standard form.

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What are the zeros of a polynomial?

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The zeros of a polynomial are the values of x for which the polynomial equals zero. They can be found by factoring the polynomial or using the quadratic formula.

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How do you find the number of possible zeros of a polynomial?

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The number of possible zeros of a polynomial is equal to its degree. For example, a cubic polynomial can have up to 3 possible zeros.

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What is a relative maximum?

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A relative maximum is a point on the graph of a function where the function value is higher than the values of the function at nearby points. It is a local peak.

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How do you determine the leading term of a polynomial?

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To determine the leading term, identify the term with the highest degree in the polynomial. For example, in $$f(x) = 4x^4 - 2x^3 + x$$, the leading term is $$4x^4$$.