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.

( 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

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

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