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Grade 9/Math/MPM1DZ/Unit 2: Polynomials.md

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+# Unit 2: Polyomials 
+
+## Introduction to Polynomials
+- A ```variable``` is a letter that represents one or more numbers    
+- An ```algebraic expression``` is a combination of variables and constants ```(e.g. x+y+6.  y + 8)```     
+- When a specific value is assigned to a variable in a algebraic expression, this is known as substitution.    
+## Methods to solve a polynomial
+  1. ```Combine like terms```
+  2. ```Dividing polynomials```
+  3. ```Multiplying polynomials```
+
+## Simplifying Alegebraic Expressions
+- An algebraic expression is an expression with numbers, variables, and operations. You may expand or simplify equations thereon.
+     
+## Factoring 
+- Two methods of solving; decomposition and criss-cross. First of all, the polynomial must be in the form of a quadratic 
+- equation (ax<sup>2</sup> + bx + c). As well, simplify the polynomial, so that all common factors are outside      
+- (e.g 5x + 10 = 5(x + 2) ).     
+
+|Type of Polynomial|Definition|
+ |:-----------------|:---------|
+ |Monomial|Polynomial that only has one term|
+ |Binomial|Polynomial that only has 2 terms|
+ |Trinomial|polynomial that only has 3 terms|
+
+ |Type|Example|
+ |:--:|:-----:|
+ |Perfect Square Trinomials| $`(a+b)^2 = a^2+2ab+b^2 or (a-b)^2 = a^2-2ab+b^2`$|
+ |Difference with Squares|$`a^2-b^2 = (a+b)(a-b)`$|
+ |Simple Trinomials|$`x^2+6x-7 = (x+7)(x-1)`$|
+ |Complex Trinomials|$`2x^2-21x-11 = (2x+1)(x-11)`$|
+ |Common Factor|$`2ab+6b+4 = 2(ab+3b+2)`$|
+ |Factor By Grouping|$`ax+ay+bx+by = (ax+ay)+(bx+by) = a(x+y)+b(x+y) = (a+b)(x+y)`$|
+
+## Shortcuts
+
+- <img src="https://image.slidesharecdn.com/factoringquadraticexpressions-120625145841-phpapp01/95/factoring-quadratic-expressions-13-728.jpg?cb=1340636365" width="500">
+
+## Foil / Rainbow Method
+- <img src = "https://calcworkshop.com/wp-content/uploads/foil-method-formula.png" width ="500">
+
+## Definitions
+- ```Term``` a variable that may have coefficient(s) or a constant     
+- ```Alebraic Expressions```: made up of one or more terms   
+- ```Like-terms```: same variables raised to the same exponent   
+
+## Tips
+- Be sure to factor fully   
+- Learn the ```criss-cross``` (not mandatory but its a really good method to factor quadratics)   
+- Learn ```long division``` (not mandatory but its a really good method to find factors of an expression)    
+- Remember your formulas   
+- Simplify first, combine like terms