Goat Math: Algebra I – Polynomials

In this article we will learn:
- What are polynomials? In this lesson we will learn about a common type of algebraic expression
- Adding polynomials: computing sums and differences of polynomials
- Multiplying monomials: Multiply and divide polynomials with one term
- Multiplying binomials: Multiply binomials together using FOIL (first, outside, inside, and last)
- Multiplying polynomials: How to multiply polynomials with many terms
- Difference of squares: A neat trick for simplifying certain binomials

Polynomials are variables raised to non-negative integer powers, multiplied by coefficients, then added together.

The degree is the biggest exponent in a polynomial. Polynomials with degree 1 are called Linear Polynomial, polynomials with degree 2 are called Quadratic Polynomial, polynomials with degree 3 are called Cubic Polynomial and polynomials with degree 4 are called Quartic Polynomial.

Leading coefficient is the coefficient for the highest power and a polynomial’s Constant Term is the coefficient of the zeroth power.

When adding/subtracting polynomials, combine like terms and when subtracting polynomials please remember to distribute the minus sign.

Monomial is a polynomial with just one term. When you are multiplying monomials with the same variable, you can add the exponents and then multiplying the coefficients. When you are dividing monomials with the same variable, you can subtract the exponents and then dividing the coefficients. Any nonzero number raised to zero power is equal to one.

Binomials is a polynomial with exactly two terms.

FOIL stand for; first, outside, inside, and last.

We use rules of exponents to simplify expressions involving exponents; when multiplying two numbers that has exponent with the same base just add exponents; when dividing two numbers has exponent with the same base, just subtract exponents; when raising powers to powers, we just multiply exponents; when a grouped of number that has exponent related to multiplication and division is raised to a power, then apply that power to all of the factors in the numerator and the denominator.