Classifying, Adding and Subtracting Polynomials

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What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 2x^3 + 3x^2 - 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 expression. For example, in the polynomial 4x^3 + 2x^2 - 7, the degree is 3.

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How do you add polynomials?

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To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5.

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How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (3x^2 + 4) - (2x^2 + 1) = (3x^2 - 2x^2) + (4 - 1) = x^2 + 3.

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What are like terms?

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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 a monomial?

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A monomial is a polynomial with only one term. For example, 5x^3 is a monomial.

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What is a binomial?

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A binomial is a polynomial with 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 three terms. For example, x^2 + 2x + 1 is a trinomial.

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How do you classify polynomials?

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Polynomials can be classified by the number of terms (monomial, binomial, trinomial) or by their degree (linear, quadratic, cubic, etc.).

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What is a constant polynomial?

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A constant polynomial is a polynomial that has no variable term, such as 5 or -3.