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^2 + 3x - 5 is a polynomial.

Front

What does it mean to add polynomials?

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Adding polynomials involves combining like terms from two or more polynomial expressions. Like terms are terms that have the same variable raised to the same power.

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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 exponent. For example, 3x^2 and 5x^2 are like terms.

Front

How do you subtract polynomials?

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To subtract polynomials, you change the sign of the terms in the polynomial being subtracted and then combine like terms.

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

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What is the coefficient in a polynomial?

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A coefficient is a numerical factor in a term of a polynomial. For example, in the term 5x^2, 5 is the coefficient.

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What is the constant term in a polynomial?

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The constant term is the term in a polynomial that does not contain any variables. For example, in the polynomial 3x^2 + 4x + 5, the constant term is 5.

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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, 3x + 5x = 8x.

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What is the result of (2x + 3) + (4x + 5)?

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The result is 6x + 8 after combining like terms.

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What is the result of (5a^2 - 3a + 2) - (2a^2 + 4)?

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The result is 3a^2 - 3a - 2 after changing the signs and combining like terms.