Unit 1 fundamental skills homework 1 exponents and polynomials – Unit 1 Fundamental Skills Homework 1: Exponents and Polynomials introduces students to the fundamental concepts of exponents and polynomials. This comprehensive guide provides a clear and concise overview of the topic, covering the properties of exponents, the different types of polynomials, polynomial operations, and polynomial factoring.

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1. Exponents

Exponents, also known as powers, are mathematical symbols that represent repeated multiplication of a number. They are written as a small number (the exponent) raised to the power of a larger number (the base).

Properties of Exponents

• Multiplication:

  a ^m× a ⁿ= a ^m+n

• Division:

  a ^m÷ a ⁿ= a ^m-n

• Power of a Power:

  (a ^m) ⁿ= a ^m×n

• Negative Exponents:

  a ^-n= 1/a ⁿ

2. Polynomials

Polynomials are algebraic expressions consisting of variables and constants combined using addition, subtraction, and multiplication. They are classified based on the number of terms:

Types of Polynomials

• Monomial:

  A polynomial with one term, e.g., 3x

• Binomial:

  A polynomial with two terms, e.g., x ²+ 2x

• Trinomial:

  A polynomial with three terms, e.g., x ³– 2x ²+ 1

3. Polynomial Operations

Polynomial operations involve performing basic arithmetic operations on polynomials:

Addition and Subtraction

To add or subtract polynomials, combine like terms with the same variable and exponent.

Multiplication

To multiply polynomials, multiply each term of one polynomial by each term of the other and simplify.

4. Polynomial Factoring: Unit 1 Fundamental Skills Homework 1 Exponents And Polynomials

Polynomial factoring involves expressing a polynomial as a product of simpler polynomials:

Methods of Factoring

• Common Factors:

  Factor out the greatest common factor from all terms.

• Grouping:

  Group terms into pairs and factor out the common factor in each pair.

• Difference of Squares:

  Factor polynomials in the form a ²– b ²as (a + b)(a – b).

5. Polynomial Applications

Polynomials have numerous applications in various fields:

Science and Engineering

• Modeling physical phenomena (e.g., projectile motion, fluid flow)

• Solving differential equations

Economics, Unit 1 fundamental skills homework 1 exponents and polynomials

• Demand and supply analysis

• Production and cost functions

Essential FAQs

What are exponents?

Exponents are mathematical symbols used to represent repeated multiplication. For example, 2 ³means 2 multiplied by itself three times, which equals 8.

What are polynomials?

Polynomials are algebraic expressions that consist of one or more terms. Each term is made up of a coefficient and a variable raised to a power.

How do you add and subtract polynomials?

To add or subtract polynomials, combine like terms. Like terms are terms that have the same variable raised to the same power.