# The Algebra of Quadratics

### By Nicholas Yiannakis

## 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.**

= 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 **G**reatest **C**ommon **F**actor (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

4. Then find two number that multiply to your product and add to 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

3, Add a 0 (x2+6x)-2=0

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**