# Polynomial Pamphlet

### Written By: Himanshu Minocha

## Factor By Grouping

There are so many ways to factor quadratic equations, but what about equations to the 3rd power and up? Lets try factoring by grouping using the example below. The objective of factoring by grouping is to take common factors from two terms. Step 1 is a visual representation of the grouping of the polynomial we are going to solve. In step 2, I factored out a 3x^3 from the first two terms and a 4 from the second two terms. Now in step 3, we add the factored out values (indicated by the double underline), then we need to multiply that by the common term (the terms underlined with one line).

## Rational Zero Theorem

Using the rational zero theorem is one way that can be used to find the roots of an equation. This theorem uses synthetic division to factor the equation, as seen in the example in my video below.

Rational Zero Theorem

## Fundamental Theorem Of Algebra

**Definition: Any function with degree n will have n number of complex zeros.**

## Quadratic Equation The quadratic equation above has a degree of 2, and has 2 complex zeros. | ## Cubic Equation This cubic equation has a degree of 3 has 3 complex zeros. | ## Quartic Equation This equation has a degree of 4, and has 4 complex zeros. |

## Summary

In this newsletter, we have covered how to factor polynomials, with degrees higher than 2, more easily by factoring by grouping. This newsletter should also have shown you how to use the Rational Zero Theorem to get the roots of a polynomial equation. Finally, this newsletter provided a definition for the Fundamental Theorem of Algebra with a few examples.

## Important Dates!

Quiz 4 12/8/15

Test 2 12/10/15