Ch 7: Exponents and Polynomials: Homework Help

1. What Are the Five Main Exponent Properties?

There are five main exponent properties, which are much like the order of operations in exponents, that give structure to simplifying expressions. Learn the formulas of the five exponent properties, including product of powers, power to a power, quotient of powers, power of a product, and power of a quotient.

2. How to Define a Zero and Negative Exponent

Exponents are not always simple integers and can take the form of negative numbers or even zero. Learn to define zero and negative exponents, explore the differences in how a negative number functions as an exponent, and understand the properties of zero and negative exponents through examples.

3. How to Simplify Expressions with Exponents

Expressions can be rewritten using exponents to be simplified visually and mathematically. Explore the use of several properties used to simplify expressions with exponents, including the product of powers, power to a power, quotient of powers, power of a product, and the zero property.

4. Rational Exponents

Rational exponents are simply a fraction representing an exponent that is rewritten as a radical expression. Explore the concept of rational exponents and understand how they are converted to radical expressions through several example problems.

5. Simplifying Expressions with Rational Exponents

Apart from being expressed as fractions, rational exponents function the same as other exponents when the properties of exponents are applied to them. Follow the steps in a series of examples to see how expressions with rational exponents are simplified in each context.

6. How to Graph Cubics, Quartics, Quintics and Beyond

Following the proper steps, the basic principles of graphing can be applied to cubics, quartics, quintics, and other polynomial functions. Learn more about basic graphing principles for polynomial functions, the importance of local maximums and minimums, and sketching for class on a graph through a detailed practice test question.

7. How to Add, Subtract and Multiply Polynomials

Polynomials can be added, subtracted, and multiplied similarly to regular numbers once the variables have been organized. Learn the steps required to apply the principles of addition, subtraction, and multiplication to polynomials through a series of example problems.

8. How to Divide Polynomials with Long Division

Polynomials can be divided using long division by dividing the first terms, multiplying the quotient by the divisor, subtracting it from the dividend, and continuously repeating the steps. Learn more about the steps for dividing polynomials with long division and why it is necessary to repeat the steps to complete the operation.

9. How to Use Synthetic Division to Divide Polynomials

Synthetic division is a shortened form of dividing polynomials by monomials that is shorter than using long division. Explore several examples of the synthetic division of polynomials and follow the correct order of steps to arrive at much simpler expressions.

10. Dividing Polynomials with Long and Synthetic Division: Practice Problems

Polynomials can be divided using both long and synthetic division, and so it is important to be comfortable using both. Learn the steps of both long and synthetic division of polynomials and use them to solve practice problems.