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 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 + 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) = 6x^2 + 3x + 5.

Front

How do you subtract polynomials?

Back

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

Front

What is the process for multiplying 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 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 + 5x + 6 is a trinomial.

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 does it mean to solve a polynomial equation?

Back

To solve a polynomial equation means to find the values of the variable that make the equation true. For example, solving x^2 - 4 = 0 gives x = 2 and x = -2.

Front

What is the zero product property?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero. For example, if (x - 2)(x + 3) = 0, then x = 2 or x = -3.