Adding and Subtracting 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 non-negative integer powers and coefficients. For example, 4x² + 3x - 5 is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions. For example, (2x + 3) + (4x + 5) = 6x + 8.

Front

What are like terms?

Back

Like terms are terms in a polynomial that have the same variable raised to the same power. For example, 3x² and 5x² are like terms, while 3x² and 4x are not.

Front

How do you subtract polynomials?

Back

To subtract polynomials, you distribute the negative sign to the second polynomial and then combine like terms. For example, (3x + 5) - (2x + 3) = 3x + 5 - 2x - 3 = x + 2.

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What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 5x² - 3x + 6, the leading coefficient is 5.

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What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, the degree of 4x² + 2x - 1 is 2.

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What is a binomial?

Back

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

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What is a trinomial?

Back

A trinomial is a polynomial that consists of exactly three terms. For example, x² + 2x + 1 is a trinomial.

Front

How do you combine like terms?

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To combine like terms, you add or subtract the coefficients of the terms that have the same variable and exponent. For example, 2x + 3x = 5x.

Front

What is the result of adding (3x - 2) + (3x² + 6x)?

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The result is 3x² + 9x - 2.