5.1 Polynomial Functions

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What is a polynomial function?

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A polynomial function is a mathematical expression that involves 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 a_n ≠ 0.

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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 expression. For example, in the polynomial 4x^3 - 2x^2 + x, the degree is 3.

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What is a monomial?

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A monomial is a polynomial with only one term. For example, 5x^2 is a monomial.

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What is a binomial?

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A binomial is a polynomial with exactly two terms. For example, 3x + 4 is a binomial.

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What is a trinomial?

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A trinomial is a polynomial with exactly three terms. For example, x^2 + 5x + 6 is a trinomial.

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What does GCF stand for in polynomial factoring?

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GCF stands for Greatest Common Factor, which is the largest factor that divides all terms in a polynomial.

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How do you determine the end behavior of a polynomial function?

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The end behavior of a polynomial function is determined by the leading coefficient and the degree of the polynomial.

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What is the leading coefficient?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It influences the direction of the graph as x approaches positive or negative infinity.

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What is the significance of the leading coefficient being positive?

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If the leading coefficient is positive, the graph of the polynomial will rise to the right as x approaches positive infinity.

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What is the significance of the leading coefficient being negative?

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If the leading coefficient is negative, the graph of the polynomial will fall to the right as x approaches positive infinity.