Update Final_Exam_Study_Sheet.md

Grade 9/Math/MFM1P1/Final_Exam_Study_Sheet.md

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 - The point where they intersect is called the point of intersection, and is when the equations equal to one another (the x and y values).
 - In terms of money, the less steep the line, the better the deal is.
 
-## Unit 8: Polynomials
+# Unit 8: Polynomials
+- `like terms`: are variables that have the same name and are raised to the same power (eg. $`x^2 \text{and } 2x^2`$)
+- `unlike terms`: are variables that have the same name and are not raised to the same power (eg $`x^2 \text{and } x`$).
 
-       
+## Summing Polynomials
+1. If there are brackets, first simplify and expand them.
+2. Simply collected the `like-terms` and simplify them.
+
+- Eg. $`(2x^2+2x+3) + (7x + x^2 - 5)`$
+- First you expand/open the brackets.
+- $`= 2x^2 + 2x + 3 + 7x + x^2 - 5`$
+- Then you collect the like terms and group them together.
+- $`= 2x^2 + x^2 + 2x + 7x + 3 - 5`$
+- Then you simplify.
+- $`= 3x^2 + 9x - 2`$
+
+## Subtracting Polynomials
+- You Simply do the same thing as summing polynomials, except to you need to be careful and apply **distributive property** with the `-1` wherever neccessary.
+- Eg. $`(4x^2 - 5) - (3 - x^2)`$
+- First open the bracets.
+- $`= 4x^2 - 5 - 3 + x^2`$
+- Group like terms together.
+- $`= 4x^2 + x^2 - 5 - 3`$
+- Simplify
+- $`= 5x^2 - 8`$
+
+## Multiplying Polynomials With A Constant
+- To do this, you simply apply the **distributive property**.
+- Eg. $`-5(x^2 - 3x + 4)`$
+- Apply distributive property.
+- $`= -5(x^2) + 5(3x) -5(4)`$
+- Then open the brackets by multiply the numbers together.
+- $`= -5x^2 + 15x - 20`$
+
+## Multiplying Polynomials With A Monomial.
+- To do this, you also use **distributive property**
+- Simply multiply everything in the polynomial by the monomial.
+- Eg.$`4x(3x^2 + 5x - 3)`$
+- Use distributive property and open the brackets.
+- $`= 4x(3x^2) + 4x(5x) + 4x(-3)`$
+- Then you reformat the numbers.
+- $`= (4)(3)(x)(x)(x) + (4)(5)(x)(x) + (-3)(4)(x)`$
+- And simplify.
+- $` = 12(x^3) + 20(x^2) + -12(x)`$
+- $` = 12x^3 + 20x^2 - 12x`$
+
+## Multiplying A Monomial With A Monomial
+- To do this, simply reformat the variables after multpilication (**distributive property)**, and simplify.
+- Eg. $`4x(-12x)`$
+- Use **distributive property** and reforat the numbers.
+- $`= (4)(-12)(x)(x)`$
+- Then you simplify.
+- $`= (-48)(x^2)`$
+- $`= -48x^2`$
+
+## Solving Equation
+- To solve a equation, is to find the **missing value** and make sure the left side and the right side are equal.
+- Remember, to solve an equation, it usually requires **multiple** steps.
+1. First simplify as much as you can.
+2. Use **distributive property** and open brackets if there are any.
+3. Regroup the terms.
+4. Simplify Again (use **distributive property** whereever nescessary).
+5. Check.
+
+
+## Tips
+- Watch out for negatives signs.
+- Make sure to label your graph CORRECTLY, with the proper x and y axis.
+
+## Credits
+- Made by Magicalsoup(James)