Adding and Subtracting Polynomials

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What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number powers and coefficients. For example, 4x^3 - 2x^2 + 7 is a polynomial.

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What does it mean to combine like terms in a polynomial?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power. For example, in the expression 3x + 4x, you can combine the like terms to get 7x.

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

Front

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 5x^4 + 3x^2 - 2, the degree is 4.

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What is a monomial?

Back

A monomial is a polynomial with only one term. For example, 7x^3 is a monomial.

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What is a binomial?

Back

A binomial is a polynomial with exactly two terms. For example, 3x + 5 is a binomial.

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What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms. For example, x^2 + 4x + 4 is a trinomial.

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What is the result of (a + b) + (c + d)?

Back

The result is a + b + c + d, which is the sum of all terms.

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

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The result is (x^2 - 2x^2) + (3x + x) = -x^2 + 4x.