Polynomials Review

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What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number powers and coefficients. It can be expressed in the form: a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants.

Front

What is the degree of a polynomial?

Back

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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How do you add polynomials?

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To add polynomials, combine like terms. Like terms are terms that have the same variable raised to the same power. For example, (2x^2 + 3x) + (4x^2 + 5) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5.

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What are like terms?

Back

Like terms are terms in a polynomial that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms, while 3x^2 and 4x are not.

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What is the process for subtracting polynomials?

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To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (3x^2 + 2x) - (x^2 + 4) = 3x^2 + 2x - x^2 - 4 = 2x^2 + 2x - 4.

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What is a monomial?

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A monomial is a polynomial with only one term. For example, 5x^3, -2xy, and 7 are all monomials.

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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 and x^2 - 5 are binomials.

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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 + 3x + 2 is a trinomial.

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How do you multiply polynomials?

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To multiply polynomials, use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial, then combine like terms.

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What is the difference between a polynomial and a rational expression?

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A polynomial is an expression that consists of variables raised to whole number powers and coefficients, while a rational expression is a fraction where the numerator and/or denominator is a polynomial.