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