# Fantastic Factoring

### By Sarah Glidden

## Objective

This newsletter I will be explaining a few different methods that can be used to factor a polynomial. I will explain factoring by grouping, the quadratic formula, and completing the square. These methods will be very helpful when needing to solve basic or very complex polynomials.

## Topics Covered

## Factor by Grouping

Factoring by grouping is used when you have 4 terms in the polynomial. Here are the steps needed:

- In order to factor take the first two terms and find a GCF or greatest common factor.
- Then do the same for the third and forth term.
- Now you take the GCF's of the two groups and put them together to create a binomial and solve for X.
- The other binomials left after the GCF's is factored out should be solved for X to get your two answers. ( The binomial left from each group should always be the same or else something was done wrong)

## Quadratic Formula

Quadratic Formula can be used to solve any quadratic equation. This is very helpful when the basic cross- box method of factoring does not work. Follow the steps below to use the formula successfully.

- First write out the equation out in standard form (ax^2+bx+c=0)
- Then plug in the values of the equation into the formula (see example for formula)
- Now simplify the equation as far as possible
- now solve for the solutions (Once done simplifying you should have two solutions because there is a square root in the equation)

*See the example below for a better understanding.

## Completing the Square

Completing the square is a process used to solve for x in a quadratic equation but this process is normally faster than using the quadratic formula. See the steps below to use completing the square.

- First make sure the equation is in standard form (ax^2 + bx + c = 0)
- Then move the c value of the equation to the right of the equal sign
- Now divide every term by the a value (Note: this step is not necessary if a=1)
- Next take half the b value and square it
- Now take this value an add it to both sides
- Then you simplify the left side into a perfect square
- Lastly solve the equation for x ( you should get two solutions)

*See the example below for more explantation

## Important Dates

Monday December 7th → Quiz 4

Thursday December 10th → Test 2

## Citations

http://www.purplemath.com/modules/sqrquad.htm

McGraw Hill Education textbook