Classifying, Adding, Subtracting, and Multiplying 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 is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 4x^3 + 2x^2 - x + 7 is in standard form.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5.

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^2 + 4) - (2x^2 + 1) = (3x^2 - 2x^2) + (4 - 1) = x^2 + 3.

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 5x^4 + 3x^2 - 2, the degree is 4.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term. For example, 7x^3 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

How do you multiply a polynomial by a monomial?

Back

To multiply a polynomial by a monomial, distribute the monomial to each term of the polynomial. For example, -x^3(2x^2 + 3x) = -2x^5 - 3x^4.

Front

What are like terms?

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.