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, 2x^2 + 3x - 5 is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power.

Front

What does it mean to subtract polynomials?

Back

Subtracting polynomials involves distributing the negative sign to the terms of the polynomial being subtracted and then combining like terms.

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.

Front

What is the result of (2x + 5y - z) + (-6x - 4y + 7z)?

Back

The result is -4x + y + 6z.

Front

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

Back

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

Front

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

Back

The result is 2x^2 + x - 10.

Front

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

Back

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

Front

What is the result of (x + 2x^2) + (4x^2 + 7x)?

Back

The result is 6x^2 + 8x.