5.1 Polynomial Functions

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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 $a_n \neq 0$.

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What are the degrees of polynomials?

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The degree of a polynomial is the highest power of the variable in the expression. Common degrees include: - Constant: Degree 0 - Linear: Degree 1 - Quadratic: Degree 2 - Cubic: Degree 3 - Quartic: Degree 4 - Quintic: Degree 5.

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Classify the polynomial: 4x^2 + 3x - 5

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Quadratic (degree 2) and Trinomial (3 terms).

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What is the end behavior of a polynomial function?

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The end behavior of a polynomial function describes how the function behaves as the input values approach positive or negative infinity. It is determined by the leading term's degree and coefficient.

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Classify the polynomial: 5x^4 - 2x^3 + x

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Quartic (degree 4) and Trinomial (3 terms).

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What is a monomial?

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A monomial is a polynomial with only one term. Example: 3x^2.

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What is a binomial?

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A binomial is a polynomial with exactly two terms. Example: 2x + 3.

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What is a trinomial?

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A trinomial is a polynomial with exactly three terms. Example: x^2 + 4x + 4.

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How do you determine the degree of a polynomial?

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The degree of a polynomial is determined by identifying the term with the highest exponent of the variable.

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What is the first step in factoring a polynomial?

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The first step is to check if there is a Greatest Common Factor (GCF) among the terms.