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Algebra I: 1,001 Practice Problems For Dummies

by Mary Jane Sterling

May 2013

Beginner

456 pages

7h 51m

English

For Dummies

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What You'd FindHow This Workbook Is OrganizedBeyond the BookWhere to Go for Additional Help
The Problems You'll Work OnWhat to Watch Out ForPlacing Real Numbers on the Number LineUsing the Absolute Value OperationAdding Signed NumbersSubtracting Signed NumbersMultiplying and Dividing Signed Numbers

The Problems You'll Work OnWhat to Watch Out ForApplying Traditional Grouping SymbolsIntroducing Some Non-Traditional Grouping SymbolsDistributing Multiplication over Addition and SubtractionAssociating Terms Differently with the Associative PropertyRearranging with the Commutative PropertyApplying More Than One Property to an Expression
The Problems You'll Work OnWhat to Watch Out ForAdding and Subtracting FractionsMultiplying FractionsDividing FractionsSimplifying Complex FractionsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsChanging Fractions to DecimalsChanging Decimals to Fractions
The Problems You'll Work OnWhat to Watch Out ForMultiplying and Dividing Exponentials with the Same BaseRaising a Power to a PowerCombining Different Operations on ExponentialsChanging the Base to Perform an OperationWorking with Scientific Notation
The Problems You'll Work OnWhat to Watch Out ForSimplifying Radical ExpressionsRationalizing DenominatorsUsing Fractional Exponents for RadicalsEvaluating Expressions with Fractional ExponentsOperating on RadicalsOperating on Factors with Fractional ExponentsEstimating Values of Radicals
The Problems You'll Work OnWhat to Watch Out ForAdding and Subtracting Like TermsMultiplying and Dividing FactorsSimplifying Expressions Using the Order of OperationsEvaluating Expressions Using the Order of OperationsOperating with FactorialsFocusing on Function Notation
The Problems You'll Work OnWhat to Watch Out ForDistributing One Term Over Sums and DifferencesDistributing Using DivisionMultiplying Binomials Using DistributingMultiplying Binomials Using FOILDistributing Binomials Over TrinomialsSquaring BinomialsRaising Binomials to the Third PowerUsing Pascal's TriangleFinding Special Products of Binomials and Trinomials
The Problems You'll Work OnWhat to Watch Out ForDividing with Monomial DivisorsMonomial Divisors and RemaindersUsing Long Division to Divide with BinomialsDividing with Binomials Using Synthetic DivisionDividing with Higher Power Divisors
The Problems You'll Work OnWhat to Watch Out ForFinding Divisors Using Rules of DivisibilityWriting Prime FactorizationsFactoring Out a GCFReducing Fractions with a Common GCF
The Problems You'll Work OnWhat to Watch Out ForFactoring the Difference of Perfect SquaresFactoring the Sum or Difference of Two Perfect CubesFactoring More Than Once
The Problems You'll Work OnWhat to Watch Out ForFactoring Out the GCF of a TrinomialFactoring Trinomials into the Products of BinomialsFactoring Quadratic-Like ExpressionsFactoring Completely Using More Than One Technique
The Problems You'll Work OnWhat to Watch Out ForFactoring by GroupingCombining Other Factoring Techniques with GroupingUsing Multiple Factoring Methods
The Problems You'll Work OnWhat to Watch Out ForSolving Linear Equations Using Basic OperationsDealing with Fractions in Linear Equations
The Problems You'll Work OnWhat to Watch Out ForApplying the Square Root Rule to Quadratic EquationsSolving Quadratic Equations Using FactoringApplying the Quadratic Formula to Quadratic EquationsCompleting the Square to Solve Quadratic EquationsWriting Complex Numbers in the Standard a + bi FormFinding Complex Solutions Using the Quadratic Formula
The Problems You'll Work OnWhat to Watch Out ForApplying Descartes's Rule of Signs to Count Real RootsApplying the Rational Root Theorem to List RootsDetermining Whether Numbers Are RootsSolving for the Roots of Polynomials
The Problems You'll Work OnWhat to Watch Out ForSolving Basic Radical EquationsChecking for Extraneous RootsSquaring Both Sides of Equations TwiceSolving Radicals with Roots Other Than Square RootsSolving Absolute Value EquationsHandling Absolute Value Equations with No Solution
The Problems You'll Work OnWhat to Watch Out ForPerforming Operations on InequalitiesWriting Inequalities Using Interval NotationChanging Interval Notation to Inequality NotationSolving Linear InequalitiesTaking on Compound InequalitiesSolving Quadratic InequalitiesFinding Solutions of Nonlinear InequalitiesRewriting and Solving Absolute Value InequalitiesDelving into Complex Inequalities
The Problems You'll Work OnWhat to Watch Out ForGetting Interested in Interest ProblemsHeating It Up with Temperature ProblemsAdding up Natural NumbersGoing the Distance with the Distance FormulaGetting the Inside Scoop with Sums of Interior AnglesAveraging Out the NumbersSumming the Squares of NumbersFinding the Terms of a SequenceAdding the Terms in an Arithmetic SequenceUsing the Formula for the Sum of CubesCompounding the Problems Involving Compound Interest
The Problems You'll Work OnWhat to Watch Out ForWorking around the Perimeter of RectanglesUsing the Area Formula for a TrapezoidTackling Area and Perimeter of a SquareSolving Problems Using the Perimeter of a TriangleWorking with the Area and Perimeter of a RectangleUsing the Formula for the Area of a HexagonGetting Pythagoras Involved in the Area of a TriangleMaking Use of the Volume of a BoxWorking with the Volume of a CylinderChanging Radians to Degrees and Degrees to RadiansDetermining the Height of an ObjectWorking with Heron's Formula for the Area of a Triangle
The Problems You'll Work OnWhat to Watch Out ForTackling Age ProblemsWorking with Consecutive IntegersGetting the Job Done on Work ProblemsCounting on Quality and Quantity ProblemsSolving Money Problems
The Problems You'll Work OnWhat to Watch Out ForPlotting Points on the Coordinate SystemDetermining the Quadrant of a PointFinding the Intercepts of a LineCalculating the slope of a line from two pointsDetermining a Line's Slope from Its EquationSketching the Graph of a Line from Its EquationSketching Lines Using Two Points
The Problems You'll Work OnWhat to Watch Out ForWriting Equations of Lines Using the Slope and a PointWriting the Equation of a Line Using Two PointsDealing with Slopes of Parallel and Perpendicular LinesFinding Equations of Lines Parallel or Perpendicular to One GivenComputing the Distance Between PointsDetermining the Midpoint
The Problems You'll Work OnWhat to Watch Out ForGraphing to Find the Intersection of Two LinesSketching the Graph of a CircleCreating the Graph of a ParabolaTransforming the Graph of a Figure

Content preview from Algebra I: 1,001 Practice Problems For Dummies

Chapter 10 Factoring Binomials

A binomial is an expression with two terms. The terms can be separated by addition or subtraction. You have four possibilities for factoring binomials: (1) factor out a greatest common factor, (2) factor as the difference of perfect squares, (3) factor as the difference of perfect cubes, and (4) factor as the sum of perfect cubes. If one of these methods doesn't work, the binomial doesn't factor when using real numbers.

The Problems You'll Work On

The problems in this chapter focus on the following:

Factoring when the two terms are the difference of perfect squares (both the numbers and the variables must be perfect squares)
Factoring when the two terms are the difference of perfect cubes (both the numbers and the variables must be perfect cubes)
Factoring when the two terms are the sum of perfect cubes (both the numbers and the variables must be perfect cubes)
Using more than one factorization technique in a problem

What to Watch Out For

When working through the steps necessary for factoring binomials, pay careful attention to the following:

Recognizing when a number is a perfect square so you can apply the factorization technique
Knowing enough of the perfect cubes to recognize them in binomials
Using the correct sign between the first and second terms of the trinomial when factoring sums and differences of cubes
Trying to factor the sum of perfect squares and mistaking it for the technique used with cubes
Using the correct exponents when ...