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 does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions. For example, (2x + 3) + (4x + 5) = 6x + 8.

Front

What does it mean to subtract polynomials?

Back

Subtracting polynomials involves taking the difference of like terms from two polynomial expressions. For example, (5x + 7) - (2x + 3) = 3x + 4.

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.

Front

How do you combine like terms?

Back

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?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in 4x^3 + 2x^2 - x, the degree is 3.

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What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 5x^4 + 3x^2, the leading coefficient is 5.

Front

How do you simplify the expression (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)?

Back

Combine like terms: (4n^4 - 4n^4) - 8n^2 - 8n + (4 - 1) = -8n^2 - 8n + 3.

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What is the result of adding (2x + 5y) + (3x - 2y)?

Back

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

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What is the result of subtracting (3x + 4y - 3z) - (2x - 6y + 7z)?

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Combine like terms: (3x - 2x) + (4y + 6y) + (-3z - 7z) = x + 10y - 10z.