Classifying, Adding, Subtracting, and Multiplying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 2x^2 + 3x + 1 is a polynomial.

Front

What is a monomial?

Back

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

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 exponents. For example, 4x^3 + 2x^2 - x + 5.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms. For example, (2x + 3) + (4x + 5) = 6x + 8.

Front

How do you subtract polynomials?

Back

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

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property (FOIL for binomials) and combine like terms. For example, (x + 2)(x + 3) = x^2 + 5x + 6.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest exponent of its variable. For example, in 4x^3 + 2x^2 - x, the degree is 3.

Front

What is a leading coefficient?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 3x^4 + 2x^3, the leading coefficient is 3.