Polynominals

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Polynominals by Mind Map: Polynominals

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)