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Algebra I – Monomials Polynomials and Factoring

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Study 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?

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Study 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:

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Study 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:

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Study 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:

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Study 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

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Study GuideAdd exponents of the same variables:Final Answer:Problem 3Step 1:Multiply coefficientsStep 2:Add exponentsFinal Answer:Problem 4

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Study GuideStep 1:Multiply coefficientsStep 2:Add exponentsFinal Answer:Problem 5Add exponents:Final Answer:Problem 6

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Study 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

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Study 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.

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Study 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:
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Document Details

University
Texas A&M University
Course
Linear Algebra
Subject
Mathematics

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