Add/subtract 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. For example, 4x^3 - 2x + 5 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 second polynomial and changing the sign of each term, then combining like terms with the first polynomial.

Front

What are like terms?

Back

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.

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How do you combine like terms?

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To combine like terms, add or subtract their coefficients while keeping the variable part the same. For example, 3x + 5x = 8x.

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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 expression. For example, in 4x^3 - 2x + 5, 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 4x^3 - 2x + 5, the leading coefficient is 4.

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

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Combine like terms: (4x - 4x) + (-2x^3 + 5x^3) + 5 = 3x^3 + 5.

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How do you simplify the expression (5x + 2) + (4x + 5)?

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Combine like terms: (5x + 4x) + (2 + 5) = 9x + 7.

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How do you simplify the expression (6b^3 + 6 - b^4) - (8b^3 - 6b^4 + 2)?

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Distribute the negative sign and combine like terms: -b^4 + 6 + 6b^4 - 8b^3 + 6b^3 - 2 = 5b^4 - 2b^3 + 4.