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Elementary Algebra

Review Exercises

Elementary AlgebraReview Exercises
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Use the Language of Algebra
    4. 1.3 Add and Subtract Integers
    5. 1.4 Multiply and Divide Integers
    6. 1.5 Visualize Fractions
    7. 1.6 Add and Subtract Fractions
    8. 1.7 Decimals
    9. 1.8 The Real Numbers
    10. 1.9 Properties of Real Numbers
    11. 1.10 Systems of Measurement
    12. Key Terms
    13. Key Concepts
    14. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations and Inequalities
    1. Introduction
    2. 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 2.2 Solve Equations using the Division and Multiplication Properties of Equality
    4. 2.3 Solve Equations with Variables and Constants on Both Sides
    5. 2.4 Use a General Strategy to Solve Linear Equations
    6. 2.5 Solve Equations with Fractions or Decimals
    7. 2.6 Solve a Formula for a Specific Variable
    8. 2.7 Solve Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Math Models
    1. Introduction
    2. 3.1 Use a Problem-Solving Strategy
    3. 3.2 Solve Percent Applications
    4. 3.3 Solve Mixture Applications
    5. 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
    6. 3.5 Solve Uniform Motion Applications
    7. 3.6 Solve Applications with Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Graphs
    1. Introduction
    2. 4.1 Use the Rectangular Coordinate System
    3. 4.2 Graph Linear Equations in Two Variables
    4. 4.3 Graph with Intercepts
    5. 4.4 Understand Slope of a Line
    6. 4.5 Use the Slope–Intercept Form of an Equation of a Line
    7. 4.6 Find the Equation of a Line
    8. 4.7 Graphs of Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Systems of Linear Equations
    1. Introduction
    2. 5.1 Solve Systems of Equations by Graphing
    3. 5.2 Solve Systems of Equations by Substitution
    4. 5.3 Solve Systems of Equations by Elimination
    5. 5.4 Solve Applications with Systems of Equations
    6. 5.5 Solve Mixture Applications with Systems of Equations
    7. 5.6 Graphing Systems of Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Polynomials
    1. Introduction
    2. 6.1 Add and Subtract Polynomials
    3. 6.2 Use Multiplication Properties of Exponents
    4. 6.3 Multiply Polynomials
    5. 6.4 Special Products
    6. 6.5 Divide Monomials
    7. 6.6 Divide Polynomials
    8. 6.7 Integer Exponents and Scientific Notation
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Factoring
    1. Introduction
    2. 7.1 Greatest Common Factor and Factor by Grouping
    3. 7.2 Factor Quadratic Trinomials with Leading Coefficient 1
    4. 7.3 Factor Quadratic Trinomials with Leading Coefficient Other than 1
    5. 7.4 Factor Special Products
    6. 7.5 General Strategy for Factoring Polynomials
    7. 7.6 Quadratic Equations
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Rational Expressions and Equations
    1. Introduction
    2. 8.1 Simplify Rational Expressions
    3. 8.2 Multiply and Divide Rational Expressions
    4. 8.3 Add and Subtract Rational Expressions with a Common Denominator
    5. 8.4 Add and Subtract Rational Expressions with Unlike Denominators
    6. 8.5 Simplify Complex Rational Expressions
    7. 8.6 Solve Rational Equations
    8. 8.7 Solve Proportion and Similar Figure Applications
    9. 8.8 Solve Uniform Motion and Work Applications
    10. 8.9 Use Direct and Inverse Variation
    11. Key Terms
    12. Key Concepts
    13. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Roots and Radicals
    1. Introduction
    2. 9.1 Simplify and Use Square Roots
    3. 9.2 Simplify Square Roots
    4. 9.3 Add and Subtract Square Roots
    5. 9.4 Multiply Square Roots
    6. 9.5 Divide Square Roots
    7. 9.6 Solve Equations with Square Roots
    8. 9.7 Higher Roots
    9. 9.8 Rational Exponents
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Quadratic Equations
    1. Introduction
    2. 10.1 Solve Quadratic Equations Using the Square Root Property
    3. 10.2 Solve Quadratic Equations by Completing the Square
    4. 10.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 10.4 Solve Applications Modeled by Quadratic Equations
    6. 10.5 Graphing Quadratic Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
  13. Index

Review Exercises

7.1 Greatest Common Factor and Factor by Grouping

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

363.

42,6042,60

364.

450,420450,420

365.

90,150,10590,150,105

366.

60,294,63060,294,630

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

367.

24x4224x42

368.

35y+8435y+84

369.

15m4+6m2n15m4+6m2n

370.

24pt4+16t724pt4+16t7

Factor by Grouping

In the following exercises, factor by grouping.

371.

axay+bxbyaxay+bxby

372.

x2yxy2+2x2yx2yxy2+2x2y

373.

x2+7x3x21x2+7x3x21

374.

4x216x+3x124x216x+3x12

375.

m3+m2+m+1m3+m2+m+1

376.

5x5yy+x5x5yy+x

7.2 Factor Trinomials of the form x2+bx+cx2+bx+c

Factor Trinomials of the Form x2+bx+cx2+bx+c

In the following exercises, factor each trinomial of the form x2+bx+cx2+bx+c.

377.

u2+17u+72u2+17u+72

378.

a2+14a+33a2+14a+33

379.

k216k+60k216k+60

380.

r211r+28r211r+28

381.

y2+6y7y2+6y7

382.

m2+3m54m2+3m54

383.

s22s8s22s8

384.

x23x10x23x10

Factor Trinomials of the Form x2+bxy+cy2x2+bxy+cy2

In the following examples, factor each trinomial of the form x2+bxy+cy2x2+bxy+cy2.

385.

x2+12xy+35y2x2+12xy+35y2

386.

u2+14uv+48v2u2+14uv+48v2

387.

a2+4ab21b2a2+4ab21b2

388.

p25pq36q2p25pq36q2

7.3 Factoring Trinomials of the form ax2+bx+cax2+bx+c

Recognize a Preliminary Strategy to Factor Polynomials Completely

In the following exercises, identify the best method to use to factor each polynomial.

389.

y217y+42y217y+42

390.

12r2+32r+512r2+32r+5

391.

8a3+72a8a3+72a

392.

4mmn3n+124mmn3n+12

Factor Trinomials of the Form ax2+bx+cax2+bx+c with a GCF

In the following exercises, factor completely.

393.

6x2+42x+606x2+42x+60

394.

8a2+32a+248a2+32a+24

395.

3n412n396n23n412n396n2

396.

5y4+25y270y5y4+25y270y

Factor Trinomials Using the “ac” Method

In the following exercises, factor.

397.

2x2+9x+42x2+9x+4

398.

3y2+17y+103y2+17y+10

399.

18a29a+118a29a+1

400.

8u214u+38u214u+3

401.

15p2+2p815p2+2p8

402.

15x2+6x215x2+6x2

403.

40s2s640s2s6

404.

20n27n320n27n3

Factor Trinomials with a GCF Using the “ac” Method

In the following exercises, factor.

405.

3x2+3x363x2+3x36

406.

4x2+4x84x2+4x8

407.

60y285y2560y285y25

408.

18a257a2118a257a21

7.4 Factoring Special Products

Factor Perfect Square Trinomials

In the following exercises, factor.

409.

25x2+30x+925x2+30x+9

410.

16y2+72y+8116y2+72y+81

411.

36a284ab+49b236a284ab+49b2

412.

64r2176rs+121s264r2176rs+121s2

413.

40x2+360x+81040x2+360x+810

414.

75u2+180u+10875u2+180u+108

415.

2y316y2+32y2y316y2+32y

416.

5k370k2+245k5k370k2+245k

Factor Differences of Squares

In the following exercises, factor.

417.

81r22581r225

418.

49a214449a2144

419.

169m2n2169m2n2

420.

64x2y264x2y2

421.

25p2125p21

422.

116s2116s2

423.

9121y29121y2

424.

100k281100k281

425.

20x212520x2125

426.

18y29818y298

427.

49u39u49u39u

428.

169n3n169n3n

Factor Sums and Differences of Cubes

In the following exercises, factor.

429.

a3125a3125

430.

b3216b3216

431.

2m3+542m3+54

432.

81x3+381x3+3

7.5 General Strategy for Factoring Polynomials

Recognize and Use the Appropriate Method to Factor a Polynomial Completely

In the following exercises, factor completely.

433.

24x3+44x224x3+44x2

434.

24a49a324a49a3

435.

16n256mn+49m216n256mn+49m2

436.

6a225a96a225a9

437.

5r2+22r485r2+22r48

438.

5u445u25u445u2

439.

n481n481

440.

64j2+22564j2+225

441.

5x2+5x605x2+5x60

442.

b364b364

443.

m3+125m3+125

444.

2b22bc+5cb5c22b22bc+5cb5c2

7.6 Quadratic Equations

Use the Zero Product Property

In the following exercises, solve.

445.

(a3)(a+7)=0(a3)(a+7)=0

446.

(b3)(b+10)=0(b3)(b+10)=0

447.

3m(2m5)(m+6)=03m(2m5)(m+6)=0

448.

7n(3n+8)(n5)=07n(3n+8)(n5)=0

Solve Quadratic Equations by Factoring

In the following exercises, solve.

449.

x2+9x+20=0x2+9x+20=0

450.

y2y72=0y2y72=0

451.

2p211p=402p211p=40

452.

q3+3q2+2q=0q3+3q2+2q=0

453.

144m225=0144m225=0

454.

4n2=364n2=36

Solve Applications Modeled by Quadratic Equations

In the following exercises, solve.

455.

The product of two consecutive numbers is 462462. Find the numbers.

456.

The area of a rectangular shaped patio 400400 square feet. The length of the patio is 99 feet more than its width. Find the length and width.

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