Adding and Subtracting Polynomials

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What is a constant polynomial?

Back

A constant polynomial is a polynomial of degree 0, which means it has no variable term. For example, 12 is a constant polynomial.

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What is a linear polynomial?

Back

A linear polynomial is a polynomial of degree 1, which has the form ax + b, where a and b are constants. For example, 2x + 3 is a linear polynomial.

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What is a quadratic polynomial?

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A quadratic polynomial is a polynomial of degree 2, which has the form ax² + bx + c, where a, b, and c are constants. For example, x² + 2x + 1 is a quadratic polynomial.

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What is a cubic polynomial?

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A cubic polynomial is a polynomial of degree 3, which has the form ax³ + bx² + cx + d, where a, b, c, and d are constants. For example, 2x³ - 3x² + x - 5 is a cubic polynomial.

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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, (3x² + 2x + 1) + (2x² - 4x - 5) = 5x² - 2x - 4.

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How do you subtract polynomials?

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To subtract polynomials, distribute the negative sign and then combine like terms. For example, (4x² + x) - (x² + 2x) = 3x² - x.

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What are like terms in polynomials?

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

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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 4x³ + 2x² - x, 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 5x² + 3x + 2, the leading coefficient is 5.

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How do you simplify the expression (x⁵ + x³) - (6x - x³ + 6x⁵)?

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To simplify, distribute the negative sign and combine like terms: (x⁵ + x³) - 6x + x³ - 6x⁵ = -5x⁵ + 2x³ - 6x.