Adding and subtracting Polynomials 1

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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, 2x^2 + 3x + 1 is a polynomial.

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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 does it mean to subtract polynomials?

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Subtracting polynomials involves taking the difference between two polynomial expressions by subtracting the coefficients of like terms.

Front

How do you identify like terms in polynomials?

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Like terms are terms that have the same variable raised to the same power. For example, in the expression 3x^2 + 5x^2, both terms are like terms because they both contain x^2.

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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 the leading coefficient of a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 5x^4 + 3x^2 - 2, the leading coefficient is 5.

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How do you combine like terms when adding polynomials?

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

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

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The result is -2x^3 + x^2 + 1.

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What is the result of (4a^3 - 8a - 4a^2) + (7a^3 - 7 - 6a)?

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The result is 11a^3 - 4a^2 - 14a - 7.

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How do you simplify the expression (3x^2 + 2x + 1) + (2x^2 - 4x - 5) + (3x - 1)?

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The simplified expression is 5x^2 + x - 5.