## Polynomial Identities as Complex Numbers

#### Aligned To Common Core Standard:

**High School** - HSN-CN.C.8

What are Polynomial Identities?
Dealing with polynomials gets challenging as the highest power of the polynomial keeps on increasing. To make it easy for students to work with polynomials, they are introduced to polynomial identities. These identities help in solving polynomials that defy rationality. These identities are true equations that are a perfect tool to solve polynomials.
There are six most common and useful polynomial identities that help us solve polynomials with ease and without losing our calm.
(a + b)^{2}=a^{2} + 2ab + b^{2}
(a + b)(c + d) = ac + bd + bc + bd
These are simple ones that we can use. For powers higher than 3, we use the following identities;
Difference of squares: a^{2}-b^{2}=(a + b)(a - b)
Sum and Difference of cubes: a^{3} ± b^{3} = (a ± b)(a^{2} ± ab + b^{2} )
x^{2} + (a + b)x + AB=(x + a)(x + b)
For solutions of quadratic equations of the form;
ax^{2} + bx + c
We use the quadratic formula to solve for the variable;
Quadratic Formula=(- b ± √(b^{2} - 4ac)) / 2a. These worksheets and lessons will help students learn how to find all possible values of variables found within complex numbers.

### Printable Worksheets And Lessons

- Binomial as a Complex Number Step-by-step Lesson- Rewrite the binomial in a complex format.

- Guided Lesson - More polynomial rewrites for you to work with.

- Guided Lesson Explanation - It is really a two step process of rationalizing and factoring in repeated fashion.

- Practice Worksheet - Ten for you to practice on as you get a real handle on the skill.

- Matching Worksheet - Match the polynomials to their complex forms.

#### Homework Sheets

The first sheet is great for students that seeing this skill for the first time.

- Homework 1 - Complex numbers are made up of several parts a real portion and an imaginary portion.
- Homework 2 - Rationalize the whole number as a form of
^{i}. - Homework 3 - These problems usually conclude with you factoring.

#### Practice Worksheets

We get a great number of teachers telling us how these particular sheets are super helpful.

- Practice 1 - Rewrite the following as complex number: x
^{2}+ 32 - Practice 2 - The imaginary portion of a complex number is easy to find, most times, because the i is hanging around it.
- Practice 3 - Breaking these into smaller parts is important.

#### Math Skill Quizzes

Each quiz mixes all the skills that you will find for this level.