## Topics

1.Expanding

2.Factoring

3.Solving

4.Completing the square

## Expanding

First we will start off by understanding what polynomials are.

Polynomials: Expressions with two numbers or variables added or subtracted together.

Example: (x+1) +/- (y-2)

But now we will discuss MULTIPLYING polynomials. Also known as expanding.

Example: (x+1) * (x+3)

x + 3x + 1x + 3

x+ 4x + 3

## Factoring

Factoring a quadratic: working backwards from the quadratic form to find the two polynomials involved

When factoring a quadratic equation with AX² of 1:

X²+ 2x + 1

X² + Bx + C

1. You find two integer that multiples to C and adds to B

2. after you find the two numbers you put them in (x ) (x ) form

EXAMPLE

X²-5X + 6

-2X-3= 6

-2+-3= -5

(X-2) (X-3)

FACTORING A QUADRATIC EQUATION WITH AX² OTHER THAN ONE:

4x²+ 4x + 1

1. you multiply A with C

2. you find a number that multiplies to C and adds to B

3. you put the two numbers inplace of B

4. you group them and take their factors as the answer

EXAMPLE

4X²+ 4X + 1

4X² + 4X + 4

2+2= 4

2X2= 4

4X² + 2X + 2X + 1

(4X² + 2X) + (2X + 1)

2X(2X + 1) 1(2X+1)

(2X+1)(2X+1)

## Solving

In order to solve a quadratic you have to use the quadratic formula

All you do is take the equation and take the x^2 as A the X as B and the Number as C

Ax^2 + Bx+ c

then you plug it into the formula below

## Completing the square

To complete the square here is what you have to do

1. factor out the first number

2.square and divide the 2nd number by 2

3.you then take the negative one and put it on the side of C

4. dont forget to multiply it by the number you have factored before leaving the bracket

5.after that you just factor the equation your left with using the tricks I showed in the "Factoring" section

Example:

2x^2 + 4x + 3

2(x^2 + 2x) +3

2(x^2+2x + 2) -4 + 2

2(x^2 +2x + 2) + 2

After this step you can just factor it and you will have the complete square