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Rotating a Parabola
Multiplying Fractions
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Mixed Numbers and Improper Fractions
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Decimals and Fractions
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Logarithmic Functions
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The Square of a Binomial
Factoring Trinomials
The Pythagorean Theorem
Solving Radical Equations in One Variable
Multiplying Binomials Using the FOIL Method
Imaginary Numbers
Solving Quadratic Equations Using the Quadratic Formula
Solving Quadratic Equations
Algebra
Order of Operations
Dividing Complex Numbers
Polynomials
The Appearance of a Polynomial Equation
Standard Form of a Line
Positive Integral Divisors
Dividing Fractions
Solving Linear Systems of Equations by Elimination
Factoring
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Functions and Graphs
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Solving Rational Equations
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Use of Parentheses or Brackets (The Distributive Law)
Multiplying and Dividing by Monomials
Solving Quadratic Equations by Graphing
Multiplying Decimals
Use of Parentheses or Brackets (The Distributive Law)
Simplifying Complex Fractions 1
Adding Fractions
Simplifying Complex Fractions
Solutions to Linear Equations in Two Variables
Quadratic Expressions Completing Squares
Dividing Radical Expressions
Rise and Run
Graphing Exponential Functions
Multiplying by a Monomial
The Cartesian Coordinate System
Writing the Terms of a Polynomial in Descending Order
Fractions
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Solving Rational Inequalities with a Sign Graph
Solving Linear Equations
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Simplifying Rational Expressions
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Intercepts of a Line
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Order of Operations
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Collecting Like Terms
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Percent of Change
Powers of ten (Scientific Notation)
Comparing Integers on a Number Line
Solving Systems of Equations Using Substitution
Factoring Out the Greatest Common Factor
Families of Functions
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Multiplying and Dividing Complex Numbers
Properties of Exponents
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Adding or Subtracting Rational Expressions with Different Denominators
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The Quadratic Formula
Writing a Quadratic with Given Solutions
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Adding and Subtracting Square Roots
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Combining Like Radical Terms
Solving Systems of Equations Using Substitution
Dividing Polynomials
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Product of a Sum and a Difference
Solving First Degree Inequalities
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Multiplying Numbers
   
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The Appearance of a Polynomial Equation

Polynomial equations sometimes come in disguise. For example, the formula: 

y = (x +1) · (x - 4)2 = (x +1) · (x - 4) · (x - 4)

does not look like a polynomial equation because it does not closely resemble the standard form of a polynomial equation given above.

However, if you FOIL this formula and carefully simplify then you can get the equation to resemble the standard form, and confirm that it is, indeed, a polynomial equation. Doing this: 

y = (x +1) · (x - 4) · (x - 4) (FOIL (x - 1) and (x - 4))
y = (x2 - 3 · x - 4) · (x - 4) (FOIL again)
y = x · (x2 - 3 · x - 4) - 4 · (x2 - 3 · x - 4) (Multiply through) 
y = x3 - 3 · x2 - 4 · x - 4 · x2 +12 · x +16 (Collect like terms)
y = x3 - 7 · x2 + 8 · x +16 (Collect like terms)

This looks exactly like the standard form of the formula for a polynomial equation. So, although the equation did not initially look very much like a polynomial equation, it turned out to be a polynomial because it was possible to expand and simplify the equation, eventually making it resemble the standard form for a polynomial equation.

 
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