Solutions for Precalculus
Problem 1SP:
Add or subtract as indicated, and simplify....Problem 4SP:
Multiply and simplify. Assume that all variable expressions represent positive real numbers....Problem 5SP:
Factor by grouping. 7cdc2+14d2cProblem 7SP:
Factor. 30m3200m2n70mn2Problem 8SP:
Factor. a.64y2+16y+1b.9m430m2n+25n2Problem 9SP:
Factor completely. a.t2121b.625z5zProblem 10SP:
Factor Completely. a.u3+27b.64v325z6Problem 11SP:
Factor completely. x5x364x2+64Problem 12SP:
Factor completely. 36m26mn9n2Problem 14SP:
Factor completely and write the answer with no negative exponents. a.11a53a4+2a3b.x4x+33/4+4x+31/4Problem 4PE:
The conjugate of 3x is .Problem 9PE:
For Exercises 9-10, determine if the expression is a polynomial. a.4a2+7b3b.34x2yc.6x+7x+5d.p2+2p5Problem 23PE:
Write the expanded from for a+b2.Problem 24PE:
Write the expanded from for a+bab.Problem 25PE:
For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) 4x54x+5Problem 27PE:
For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) 3w27z3w2+7zProblem 28PE:
For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) 9v3+2u9v32uProblem 30PE:
For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) 16n45p416n+45p4Problem 31PE:
For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) 5m32Problem 32PE:
For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) 7v22Problem 33PE:
For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) 4t2+3p32Problem 34PE:
For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) 2a2+11b32Problem 36PE:
For Exercises 25-38, perform the indicated operations and simplify. (See Example 3) p23Problem 39PE:
Suppose that x represents the smaller of two consecutive integers. a. Write a polynomial that...Problem 40PE:
Suppose that x represents the larger of two consecutive odd integers. a. Write a polynomial that...Problem 41PE:
For Exercises 41-48, simplify each expression. y+722y32Problem 42PE:
For Exercises 41-48, simplify each expression. x426x+12Problem 43PE:
For Exercises 41-48, simplify each expression. xn+3xn7Problem 44PE:
For Exercises 41-48, simplify each expression. yn+4yn5Problem 46PE:
For Exercises 41-48, simplify each expression. wnym2Problem 49PE:
For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive...Problem 51PE:
For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive...Problem 54PE:
For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive...Problem 55PE:
For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive...Problem 58PE:
For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive...Problem 59PE:
For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive...Problem 62PE:
For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive...Problem 63PE:
For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive...Problem 65PE:
For Exercises 49-66, multiply and simplify. Assume that all variable expressions represent positive...Problem 76PE:
For Exercises 73-76, factor out the indicated common factor. Factorout7a3b.14a4b3+21a3b27a3bProblem 131PE:
For Exercises 131-142, Factors completely. Write the answer with positive exponents only. (See...Problem 135PE:
For Exercises 131-142, Factors completely. Write the answer with positive exponents only. (See...Problem 139PE:
For Exercises 131-142, Factors completely. Write the answer with positive exponents only. (See...Problem 140PE:
For Exercises 131-142, Factors completely. Write the answer with positive exponents only. (See...Problem 146PE:
Explain the similarity in the process to factor out the GCF in the following two expressions....Problem 150PE:
We say that the expression x24 is factorable over the integers as x+2x2 . Notice that the constant...Problem 152PE:
We say that the expression x24 is factorable over the integers as x+2x2 . Notice that the constant...Problem 153PE:
For Exercises 153-156, determine if the statement is true or false. If a statement is false, Explain...Problem 154PE:
For Exercises 153-156, determine if the statement is true or false. If a statement is false, Explain...Problem 155PE:
For Exercises 153-156, determine if the statement is true or false. If a statement is false, Explain...Problem 156PE:
For Exercises 153-156, determine if the statement is true or false. If a statement is false, Explain...Problem 1PRE:
Many expressions in algebra look similar but the methods used to simplify the expressions may be...Problem 6PRE:
Many expressions in algebra look similar but the methods used to simplify the expressions may be...Problem 9PRE:
Many expressions in algebra look similar but the methods used to simplify the expressions may be...Browse All Chapters of This Textbook
Chapter R - Review Of PrerequisitesChapter R.1 - Sets And The Real Number LineChapter R.2 - Exponents And RadicalsChapter R.3 - Polynomials And FactoringChapter R.4 - Rational Expressions And More Operations On RadicalsChapter R.5 - Equations With Real SolutionsChapter R.6 - Complex Numbers And More Quadratic EquationsChapter R.7 - Applications Of EquationsChapter R.8 - Linear, Compound, And Absolute Value InequalitiesChapter 1 - Functions And Relations
Chapter 1.1 - The Rectangular Coordinate System And Graphing UtilitiesChapter 1.2 - CirclesChapter 1.3 - Functions And RelationsChapter 1.4 - Linear Equations In Two Variables And Linear FunctionsChapter 1.5 - Applications Of Linear Equations And ModelingChapter 1.6 - Transformations Of GraphsChapter 1.7 - Analyzing Graphs Of Functions And Piecewise-defined FunctionsChapter 1.8 - Algebra Of Functions And Function CompositionChapter 2 - Polynomial And Rational FunctionsChapter 2.1 - Quadratic Functions And ApplicationsChapter 2.2 - Introduction To Polynomial FunctionsChapter 2.3 - Division Of Polynomials And The Remainder And Factor TheoremsChapter 2.4 - Zeros Of PolynomialsChapter 2.5 - Rational FunctionsChapter 2.6 - Polynomial And Rational InequalitiesChapter 2.7 - VariationChapter 3 - Exponential And Logarithmic FunctionsChapter 3.1 - Inverse FunctionsChapter 3.2 - Exponential FunctionsChapter 3.3 - Logarithmic FunctionsChapter 3.4 - Properties Of LogarithmsChapter 3.5 - Exponential And Logarithmic Equations And ApplicationsChapter 3.6 - Modeling With Exponential And Logarithmic FunctionsChapter 4 - Trigonometric FunctionsChapter 4.1 - Angles And Their MeasureChapter 4.2 - Trigonometric Functions Defined On The Unit CircleChapter 4.3 - Right Triangle TrigonometryChapter 4.4 - Trigonometric Functions Of Any AngleChapter 4.5 - Graphs Of Sine And Cosine FunctionsChapter 4.6 - Graphs Of Other Trigonometric FunctionsChapter 4.7 - Inverse Trigonometric FunctionsChapter 5 - Analytic TrigonometryChapter 5.1 - Fundamental Trigonometric IdentitiesChapter 5.2 - Sum And Difference FormulasChapter 5.3 - Double-angle, Power-reducing, And Half-angle FormulasChapter 5.4 - Product-to-sum And Sum-to-product FormulasChapter 5.5 - Trigonometric EquationsChapter 6 - Applications Of Trigonometric FunctionsChapter 6.1 - Applications Of Right TrianglesChapter 6.2 - The Law Of SinesChapter 6.3 - The Law Of CosinesChapter 6.4 - Harmonic MotionChapter 7 - Trigonometry Applied To Polar Coordinate Systems And VectorsChapter 7.1 - Polar CoordinatesChapter 7.2 - Graphs Of Polar EquationsChapter 7.3 - Complex Numbers In Polar FormChapter 7.4 - VectorsChapter 7.5 - Dot ProductChapter 8 - Systems Of Equations And InequalitiesChapter 8.1 - Systems Of Linear Equations In Two Variables And ApplicationsChapter 8.2 - Systems Of Linear Equations In Three Variables And ApplicationsChapter 8.3 - Partial Fraction DecompositionChapter 8.4 - Systems Of Nonlinear Equations In Two VariablesChapter 8.5 - Inequalities And Systems Of Inequalities In Two VariablesChapter 8.6 - Linear ProgrammingChapter 9 - Matrices And Determinants And ApplicationsChapter 9.1 - Solving Systems Of Linear Equations Using MatricesChapter 9.2 - Inconsistent Systems And Dependent EquationsChapter 9.3 - Operations On MatricesChapter 9.4 - Inverse Matrices And Matrix EquationsChapter 9.5 - Determinants And Cramer’s RuleChapter 10 - Analytic GeometryChapter 10.1 - The EllipseChapter 10.2 - The HyperbolaChapter 10.3 - The ParabolaChapter 10.4 - Rotation Of AxesChapter 10.5 - Polar Equations Of ConicsChapter 10.6 - Plane Curves And Parametric EquationsChapter 11 - Sequences, Series, Induction, And ProbabilityChapter 11.1 - Sequences And SeriesChapter 11.2 - Arithmetic Sequences And SeriesChapter 11.3 - Geometric Sequences And SeriesChapter 11.4 - Mathematical InductionChapter 11.5 - The Binomial TheoremChapter 11.6 - Principles Of CountingChapter 11.7 - Introduction To Probability
Book Details
Julie Miller wrote her developmental math series because students were coming into her Precalculus course underprepared. They weren’t mathematically mature enough to understand the concepts of math nor were they fully engaged with the material. She began her developmental mathematics offerings with intermediate algebra to help bridge that gap. The Precalculus series is a carefully constructed end to that bridge that uses the highly effective pedagogical features from her fastest growing developmental math series. What sets Julie Miller’s series apart is that it addresses course issues through an author-created digital package that maintains a consistent voice and notation throughout the program. This consistency--in videos, PowerPoints, Lecture Notes, and Group Activities--coupled with the power of ALEKS and Connect Hosted by ALEKS, ensures that students master the skills necessary to be successful in Precalculus and can carry them through to the calculus sequence.
Sample Solutions for this Textbook
We offer sample solutions for Precalculus homework problems. See examples below:
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