Adding and Subtracting Polynomials

Front

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, 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. Like terms are terms that have the same variable raised to the same power.

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 subtract polynomials?

Back

To subtract polynomials, you change the signs of the terms in the polynomial being subtracted and then combine like terms.

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

Front

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

Back

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

Front

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

Back

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

Front

How do you combine the polynomials (x^5 + x^3) - (6x - x^3 + 6x^5)?

Back

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

Front

What is the simplified form of (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)?

Back

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

Front

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

Back

The result is 3x^2 - x.