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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). - 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. - 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)