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, combined using addition, subtraction, and multiplication.

Front

What are the degrees of polynomials?

Back

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

Front

How do you add polynomials?

Back

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

Front

What are like terms in polynomials?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to the terms of the polynomial being subtracted, then combine like terms.

Front

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

Back

The result is 3x^2 - x.

Front

What is the sum of (6x + 4x^4 - 3x^2) + (7x^4 + 5x^2 + 8x)?

Back

The sum is 11x^4 + 2x^2 + 14x.

Front

What is the process to simplify (3y^2 + y^3 - 5) + (4y^2 - 4y + 2y^3 + 8)?

Back

Combine like terms: y^3 terms, y^2 terms, y terms, and constant terms to get 3y^3 + 7y^2 - 4y + 3.

Front

What is the result of (x^5 + x^3) - (6x - x^3 + 6x^5)?

Back

The result is -5x^5 + 2x^3 - 6x.

Front

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

Back

Distribute the negative sign and combine like terms to get -8n^2 - 8n + 3.