# Polynominals

# Polynominals

by Jessi Bee
# 1. Definitions

## 1.1. Term - an expression formed from the product of numbers and/or variables.

## 1.2. Variables - a letter used to represent an unknown number

## 1.3. Coefficient - a non-changing variable

## 1.4. Degree - the sum of exponents on the variables

## 1.5. Polynominal - an expression where there is a sum of terms each of which is the product of a constant and one or more variables

# 2. Multiplication

## 2.1. 2y x 3y = 6y^2

## 2.2. (x+1)(x-1) = x^2-1

## 2.3. x(x^2+2x+1) = x^3+2x^2+x

## 2.4. Multiplying using tiles

## 2.5. (x2 + 2x + 3)(2x2 – 3x + 1) = 2x4 + x3 + x2 – 7x + 3

## 2.6. Multiply the expressions together

# 3. Factoring

## 3.1. 16x2y – 24xy3 + 8xy = (8xy)(2x – 3y2 + 1)

## 3.2. Simplifying expressions to their most factored forms

## 3.3. New node

# 4. Nomials

## 4.1. Monomials - an expression with only one term

## 4.2. Binomials - an expression with two terms

## 4.3. Trinomials - an expression with three terms

## 4.4. Polynomials - an expression with four or more terms

# 5. Algebraically

## 5.1. To solve an expression using mathematical terms such as with numbers and signs.

## 5.2. Using numbers and terms

# 6. Algebra Tiles

## 6.1. Using a model of math tiles to solve an equation

## 6.2. Using tiles

# 7. Greatest Common Factor/ Multiples

## 7.1. 12 = 3 x 4 = 3 x 2 x 2 = 3 x 2^2

## 7.2. 18 = 3 x 6 = 3 x 3 x 2 = 3^2 x 2

## 7.3. Factoring

## 7.4. 4 = 4, 8, 12, 16, 24, 28, 32...

## 7.5. 6 = 6, 12...

# 8. Example Multiplication of Polynomials

## 8.1. 2(x+1)

## 8.2. x(x-3) + 4(2+x)

## 8.3. (x^2+1)(x+3)

## 8.4. x^2 + 5(x^2-2x+1)

## 8.5. (x^2+2)(x^2+6x-9)

# 9. Example Factoring of Polynomials

## 9.1. (x^2-9)

## 9.2. (x^2+5x-25)

## 9.3. (x^3+x^2+2x+2)