# Polynomial Worksheets

What are Polynomials? This topic is the fundamental basis of the subject of algebra. Polynomials consist of variables and constants both. The variables can have a singular power, or they can have multiple powers. The standardized formula of a polynomial expression is {ax} _1^{n}, while the number of variables increases depending on the expression.
However, they are restricted only to have positive integer values in their power. Let us consider a few examples where we will identify which of them are polynomials.
6x^{2} (polynomial) | √x + 2x (Not a polynomial because it has radical on the variable) | 1/x^{2} (Not a polynomial because the variable is present at the denominator)
This series of worksheets are being seen to a much greater degree now that the curriculum has been adopted by the mass majority of communities. You will learn how to manipulate these types of expressions in a wide variety of ways and apply them to other common theories.

- Adding and Subtracting Rational Expressions - This is usually where start with these types of problems. Just pay attention to the rules in place. They will apply across the board regardless of how many terms you are working with.
- Applying the Remainder Theorem - This helps you entirely avoid performing polynomial long division when you are finding factors. This is an awesome shortcut to help you determine quotients.
- Binomial Theorem for Expansion - This gets more difficult as the size of the exponent increases. Though this is aimed at binomials, the outcomes will roll into this neck of the woods.
- Graphing Polynomial Functions - This is a more advanced skill that will serve you well when analyzing data of all types.
- Identifying Zeros of Binomials - This happens when we set the equation equal to zero. The applications of this are numerous.
- Interpret the Context of Expressions - This helps students learn to evaluate the overall situation that has presented itself in the problem. The better you understand the reason behind something, the easier it is to work with.
- Multiplying and Dividing Rational Expressions - We show students how to find the product and quotients in these types of problems.
- Polynomial Addition and Subtraction - Simple yet effective techniques are presented here. This will also help you learn how to quickly reduce terms and come to swift conclusion.
- Polynomial Division - Students explore how to find the value of quotients. This will expand to more advanced skills.
- Polynomial Multiplication - In this case, we are distributing the terms from the first polynomial to the second.
- Polynomial Identities as Complex Numbers - As you get into upper High School math the topics become more theoretical. You will see the application of this skill the further you go with it.
- Proving Polynomial Identities - We look at all the possible values for variables in an equation. You will also begin to under the reasoning behind it.
- Rewriting Rationale Expression - How to rearrange these things to make them work better for your own purposes. Being able to make them bend to your will is a powerful math skill to master.

### Why Are Polynomials Important?

These algebraic expressions are helpful tools for helping us solve many real-world problems. They are especially helpful modeling physical phenomena and helping us forecast possible outcomes in a multitude of different industries and sectors. When building laborers are constructing any two-dimensional structure, polynomials come in handy to determine the amount of materials that are required, and the cost associated with both purchasing the materials.

Economists and financial planners use this type of math to determine the potential growth of an investment or the degree to which a financial liability can hurt or help an organization. In the world of finance, the toughest decisions are made before anything is wrong or right. Polynomials are used to build complex budgets that affect the lives of millions of people in all countries around the world.

Scientists and engineers use this type of math to model trajectory paths of just about anything flying through the air from a hot air balloon to a space shuttle. They are especially helpful to understand energy transfer and voltage differences. In chemistry this math is used to understand the amount of pressure exert by a gas in certain containers.

## What Is the Difference Between a Polynomial Equation, Expression, and Inequality?

This is a very common question that most students have. While it is obvious to most teachers and adults, for that matter, many students simply do not get it. It is merely being a bit overwhelmed with a small portion of the algebra related vocabulary. We feel it is important to take the time to blatantly cover this simple concept with all of them. Students are simply getting confused because all three start with the same word. It has absolutely nothing to do with that word at all. The word polynomial consists of two subset words poly- (signifying many) and -nomial (indicating name, but in this case, it means math terms). So, it just means containing many terms. The difference really lies between equations, expressions, and functions. The most primitive being an expression is a math term or series of terms that has no relational symbol present. Equations are math declarations that include an expression and an equals symbol. Inequalities are just that, not equal. They are math statements that contain expressions and not equal or inequality symbols. We encourage all teachers to take the time to explain this simple concept.