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

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from each polynomial. For example, (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

Front

What does it mean to subtract polynomials?

Back

Subtracting polynomials involves taking the difference of like terms. For example, (5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2.

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 multiply polynomials?

Back

To multiply polynomials, use the distributive property (FOIL for binomials) to multiply each term in the first polynomial by each term in the second polynomial.

Front

What are like terms in a polynomial?

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.

Front

What is the degree of a polynomial?

Back

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

Front

How do you combine like terms?

Back

To combine like terms, add or subtract the coefficients of the terms that have the same variable and exponent. For example, 3x + 5x = 8x.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, such as 4x^3 or -7.

Front

What is a binomial?

Back

A binomial is a polynomial with two terms, such as 3x + 5 or x^2 - 4.