Adding, Subtracting, Multiplying, and Dividing 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, 4x^3 + 3x^2 - 2x + 1 is a polynomial.

Front

What are the degrees of polynomials?

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 - 7, the degree is 4.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (3x^2 + 2x) + (4x^2 + 5) = (3x^2 + 4x^2) + 2x + 5 = 7x^2 + 2x + 5.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms. For example, 3x + 5 is a binomial.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms. For example, x^2 + 3x + 2 is a trinomial.

Front

What is the process of subtracting polynomials?

Back

To subtract polynomials, change the sign of the polynomial being subtracted and then add. For example, (5x^2 + 3) - (2x^2 + 4) = (5x^2 - 2x^2) + (3 - 4) = 3x^2 - 1.

Front

How do you multiply polynomials?

Back

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

Front

What is the result of multiplying (x + 2)(x + 3)?

Back

The result is x^2 + 5x + 6.

Front

What is a quartic polynomial?

Back

A quartic polynomial is a polynomial of degree four. For example, 2x^4 + 3x^3 - x + 5 is a quartic polynomial.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms. For example, 4x^3 + 2x^2 - x + 7 is in standard form.