## Topics

Expanding

Factoring

Solving

Completing the Square

## Expanding

The definition of polynomials-

Expressions with two numbers or variables added or subtracted together.

Example:

(x+5) (3y-5)

A common method used when expanding quadratic equations is FOIL.

FOIL stands for (First, Outside, Inside, Last)

This method is one of the easiest was to expand a quadratic equation.

Heres and example of expanding a quadratic equation.

( x + 3 ) ( x + 2 )
= x2 + 2x + 3x + 6

= x2 + 5x + 6

## Common Factoring

The complete opposite of expanding

If every term of a polynomial is divisible by the same constant, this constant is also called a common factor

A polynomial is not considered to be completely factored until the Greatest Common Factor (GCF) has been factored out

Example

4x+20 = 2(2x+10) -----> Not Completely Factored

4x+20 = 4(x+5)-----> Completely Factored

## Complex Factoring ( With Decomposition)

ax2 + bx + c

1. Take A and C and multiply them

2. This will then be you product

3. Then take your middle term and use it as your sum

## Completing the Square

X2+6x-2

1. Block of the first two terms(x2+6x)-2

2. Factor out the A if possible

4. Take the middle term and divide by two. Then square it x2+6x+9-9-2

5. Bring out the negatives(x2+6x+9)-9-2

You Did it!

## Solving

When you have an equation equal to zero you need to find X

Example-

(x – 3)(x – 4) = 0

For the first bracket make x=For the second bracket make x=4

❤² How to Solve Quadratic Equations By Factoring (mathbff)