Polynomial Review

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number powers and coefficients. For example, 3x^2 + 2x - 5 is a polynomial.

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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 the polynomial 4x^3 + 2x^2 - x + 7, the degree is 3.

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What is polynomial long division?

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Polynomial long division is a method used to divide a polynomial by another polynomial of the same or lower degree, similar to numerical long division.

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What is synthetic division?

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Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor of the form (x - c).

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What is the Remainder Theorem?

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The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder of that division is f(c).

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What is the Factor Theorem?

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The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

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How do you evaluate a polynomial function?

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To evaluate a polynomial function f(x) at a specific value of x, substitute the value of x into the polynomial and simplify.

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What is the difference between a monomial, binomial, and trinomial?

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A monomial is a polynomial with one term, a binomial has two terms, and a trinomial has three terms. For example, 5x (monomial), 3x + 2 (binomial), 2x^2 + 3x - 1 (trinomial).

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What is the standard form of a polynomial?

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The standard form of a polynomial is written in descending order of the degree of its terms. For example, 4x^3 + 2x^2 - x + 7 is in standard form.

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What is a zero of a polynomial?

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A zero of a polynomial is a value of x for which the polynomial evaluates to zero. For example, if f(x) = x^2 - 4, then x = 2 and x = -2 are zeros.