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 + 3) - (2x + 1) = 3x + 2.

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

Back

The simplified expression is -8n^2 - 8n + 3.

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

Back

The result is 5x + 3y.

Front

How do you find the difference of (3x + 4y - 3z) - (2x - 6y + 7z)?

Back

The difference is x + 10y - 10z.

Front

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

Back

The result is -x^2 - 6x + 8.

Front

How do you add the polynomials (3y^2 + y^3 - 5) + (4y^2 - 4y + 2y^3 + 8)?

Back

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

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