Adding and Subtracting Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

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 changing the signs of the terms in 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.

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.

Front

What is the perimeter of a rectangle with length x and width 2x + 5?

Back

The perimeter is 2(x + (2x + 5)) = 6x + 10.

Front

How do you combine the terms -7xy + x + y + x - 3xy?

Back

The combined expression is -10xy + 2x + y.

Front

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

Back

The result is 5x^2 - 2y^2.

Front

How do you simplify the expression (x^5 + x^3) - (6x - x^3 + 6x^5)?

Back

The simplified expression is -5x^5 + 2x^3 - 6x.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression.