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 non-negative integer powers and coefficients. It can be expressed in the form: a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants.

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What are the degrees of the polynomials in the expression (4a^3 - 8a - 4a^2) + (7a^3 - 7 - 6a)?

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The degrees of the polynomials are: 4a^3 has degree 3, -4a^2 has degree 2, -8a has degree 1, and -7 has degree 0. The highest degree in the entire expression is 3.

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How do you add polynomials?

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To add polynomials, combine like terms by adding their coefficients. Like terms are terms that have the same variable raised to the same power.

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What is a like term?

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Like terms are terms in a polynomial that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms, while 3x^2 and 4x are not.

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What is the result of adding (3x^2 + 2x + 1) + (2x^2 - 4x - 5) + (3x - 1)?

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The result is 5x^2 + x - 5.

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What is the process for subtracting polynomials?

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To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms.

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

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The result is a^2 + 8a + 7.

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What is the sum of (3y^2 + y^3 - 5) + (4y^2 - 4y + 2y^3 + 8)?

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The sum is 3y^3 + 7y^2 - 4y + 3.

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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 + 5, the degree is 3.

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What does it mean to simplify a polynomial expression?

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To simplify a polynomial expression means to combine like terms and express the polynomial in its simplest form.