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 are like terms?

Back

Like terms are terms in a polynomial that have the same variable raised to the same power. For example, 2x and 3x are like terms, while 2x and 2y are not.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (3x + 4) + (2x + 5) = (3x + 2x) + (4 + 5) = 5x + 9.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (3x + 4) - (2x + 5) = (3x - 2x) + (4 - 5) = x - 1.

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 a monomial?

Back

A monomial is a polynomial with only one term. For example, 5x^2 is a monomial.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms. For example, 3x + 4 is a binomial.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms. For example, x^2 + 2x + 1 is a trinomial.

Front

What is the result of (3x + 4y - 3z) - (2x - 6y + 7z)?

Back

x + 10y - 10z.

Front

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

Back

3y^3 + 7y^2 - 4y + 3.