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

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 + 4) = 5x^2 - 2x^2 + 3 - 4 = 3x^2 - 1.

Front

What is the product of two binomials?

Back

The product of two binomials can be found using the distributive property (FOIL method). For example, (a + b)(c + d) = ac + ad + bc + bd.

Front

What is the difference between a polynomial and a monomial?

Back

A monomial is a polynomial with only one term. For example, 4x^3 is a monomial, while 4x^3 + 2x is a polynomial.

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property to multiply each term in one polynomial by each term in the other. For example, (2x)(3x^2) = 6x^3.

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 + 5 is in standard form.