CramX Logo
RegisterLog in
Algebra I – Monomials Polynomials and Factoring - Document preview page 1

Algebra I – Monomials Polynomials and Factoring - Page 1

Document preview content for Algebra I – Monomials Polynomials and Factoring

Algebra I – Monomials Polynomials and Factoring

This document provides study materials related to Algebra I – Monomials Polynomials and Factoring. It may include explanations, summarized notes, examples, or practice questions designed to help students understand key concepts and review important topics covered in their coursework.

Students studying Mathematics or related courses can use this material as a reference when preparing for assignments, exams, or classroom discussions. Resources on CramX may include study notes, exam guides, solutions, lecture summaries, and other academic learning materials.

Nivaldo
Contributor
0.0
0
2 months ago
Preview (10 of 86 Pages)
100%
Log in to unlock
Page 1 of 86
Algebra I – Monomials Polynomials and Factoring - Page 1 preview imageStudy GuideAlgebra–Monomials Polynomials and Factoring1.MonomialsWhat is a Monomial?Amonomialis an algebraic expression that hasonly one term.Atermis a number, a variable, or a combination of numbers and variables that are multipliedtogether.Examples of Monomials•(9x)•(4a2)•(3mpx2)Each of these hasonly one term, so they are monomials.Thenumber in front of the variableis called thenumerical coefficient.Example:•In9x, the coefficient is9.Adding and Subtracting MonomialsWhen adding or subtracting monomials, you must follow one important rule:You canonly combine like terms.What are Like Terms?
Page 2 of 86
Algebra I – Monomials Polynomials and Factoring - Page 2 preview imageStudy GuideLike terms have:•Thesame variables•Thesame exponentsWhen terms are alike:•Add or subtract the coefficients•Keep the variables the sameExample 1Perform the operation:Step-by-step:1.Divide the coefficients(15 ÷-3 =-5)2.The variables cancel because they are the same.Final Answer:Example 2Both terms containx, so they are like terms.Add the coefficients:
Page 3 of 86
Algebra I – Monomials Polynomials and Factoring - Page 3 preview imageStudy GuideFinal Answer:Example 3Step-by-step:1.Divide the coefficients(9 ÷-3 =-3)2.(y) cancels out.Final Answer:Example 4Step-by-step:1.Combine like terms:
Page 4 of 86
Algebra I – Monomials Polynomials and Factoring - Page 4 preview imageStudy Guide2.Subtract (3q):3.Subtracting a negative becomes addition:Final Answer:Multiplying MonomialsWhen multiplying monomials, remember this rule:Add the exponents when the base is the same.This rule comes from the laws of exponents.ExamplesAnother example:Important RuleTo multiply monomials:
Page 5 of 86
Algebra I – Monomials Polynomials and Factoring - Page 5 preview imageStudy Guide1.Multiply thenumbers (coefficients)2.Add the exponentsof variables with the same base.Example 2:Multiplying MonomialsMultiply the following expressions.Problem 1Add the exponents:Final Answer:Problem 2
Page 6 of 86
Algebra I – Monomials Polynomials and Factoring - Page 6 preview imageStudy GuideAdd exponents of the same variables:Final Answer:Problem 3Step 1:Multiply coefficientsStep 2:Add exponentsFinal Answer:Problem 4
Page 7 of 86
Algebra I – Monomials Polynomials and Factoring - Page 7 preview imageStudy GuideStep 1:Multiply coefficientsStep 2:Add exponentsFinal Answer:Problem 5Add exponents:Final Answer:Problem 6
Page 8 of 86
Algebra I – Monomials Polynomials and Factoring - Page 8 preview imageStudy GuideAdd exponents:Final Answer:Raising Monomials to a PowerSometimes a monomial is raised to a power.In this case:Multiply the exponents by the power.Example rule:This means every exponent inside the monomial gets multiplied by the power outside.Powers and Division of MonomialsExample 3:Simplifying PowersSometimes a monomial is raised to a power.To simplify expressions like this, we apply therules of exponents.Rule
Page 9 of 86
Algebra I – Monomials Polynomials and Factoring - Page 9 preview imageStudy GuideWhen a power is raised to another power,multiply the exponents.Example 3Simplify the following expressions.1.Multiply the exponents:2.Multiply each exponent by4:Final answer:3.
Page 10 of 86
Algebra I – Monomials Polynomials and Factoring - Page 10 preview imageStudy GuideApply the power toeach partof the monomial:Final answer:Dividing MonomialsWhen dividing monomials that have thesame base, we use a simple rule.RuleSubtract the exponent of the divisor from the exponent of the dividend.Example 4:Dividing MonomialsDivide the following expressions.Problem 1Subtract the exponents:
Preview Mode

This document has 86 pages. Sign in to access the full document!

Study Now!

X-Copilot AI
Unlimited Access
Secure Payment
Instant Access
24/7 Support
Document Chat

Document Details

University
Texas A&M University
Course
Linear Algebra
Subject
Mathematics

Related Documents

View all
Quick Guides

Algebra I – Word Problems

Quick Guides

Algebra I – Terminology Sets and Expressions

Quick Guides

Algebra I – Signed Numbers Fractions and Percents

Quick Guides

Algebra I – Roots and Radicals

Quick Guides

Algebra I – Quadratic Equations

Quick Guides

Algebra I – Preliminaries and Basic Operations

Quick Guides

Algebra I – Inequalities Graphing and Absolute Value

Quick Guides

Algebra I – Functions and Variations

Quick Guides

Algebra I – Equations with Two Variables

Quick Guides

Algebra I – Equations Ratios and Proportions