A2 - BW 12/5-12/6 Adding and Subtracting Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 3x^2 + 2x - 5 is a polynomial.

Front

What are like terms?

Back

Like terms are terms that have the same variable raised to the same power. For example, 2x and 3x are like terms, while 2x and 2x^2 are not.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5x) = (2+4)x^2 + (3+5)x = 6x^2 + 8x.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (5x + 2) - (3x + 4) = 5x + 2 - 3x - 4 = (5-3)x + (2-4) = 2x - 2.

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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 a coefficient in a polynomial?

Back

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 result of adding (x + 2x^2) + (4x^2 + 7x)?

Back

The result is 6x^2 + 8x.

Front

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

Back

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

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What is the result of simplifying (5x + x^2 - 4) - (4x - x^2 + 6)?

Back

The result is 2x^2 + x - 10.

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What is the result of simplifying (6x + 4x^4 - 3x^2) + (7x^4 + 5x^2 + 8x)?

Back

The result is 11x^4 + 2x^2 + 14x.