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Intermediate Algebra 2e

Review Exercises

Intermediate Algebra 2eReview Exercises
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Use the Language of Algebra
    3. 1.2 Integers
    4. 1.3 Fractions
    5. 1.4 Decimals
    6. 1.5 Properties of Real Numbers
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations
    1. Introduction
    2. 2.1 Use a General Strategy to Solve Linear Equations
    3. 2.2 Use a Problem Solving Strategy
    4. 2.3 Solve a Formula for a Specific Variable
    5. 2.4 Solve Mixture and Uniform Motion Applications
    6. 2.5 Solve Linear Inequalities
    7. 2.6 Solve Compound Inequalities
    8. 2.7 Solve Absolute Value Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Graphs and Functions
    1. Introduction
    2. 3.1 Graph Linear Equations in Two Variables
    3. 3.2 Slope of a Line
    4. 3.3 Find the Equation of a Line
    5. 3.4 Graph Linear Inequalities in Two Variables
    6. 3.5 Relations and Functions
    7. 3.6 Graphs of Functions
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Systems of Linear Equations
    1. Introduction
    2. 4.1 Solve Systems of Linear Equations with Two Variables
    3. 4.2 Solve Applications with Systems of Equations
    4. 4.3 Solve Mixture Applications with Systems of Equations
    5. 4.4 Solve Systems of Equations with Three Variables
    6. 4.5 Solve Systems of Equations Using Matrices
    7. 4.6 Solve Systems of Equations Using Determinants
    8. 4.7 Graphing Systems of Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Polynomials and Polynomial Functions
    1. Introduction
    2. 5.1 Add and Subtract Polynomials
    3. 5.2 Properties of Exponents and Scientific Notation
    4. 5.3 Multiply Polynomials
    5. 5.4 Dividing Polynomials
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Factoring
    1. Introduction to Factoring
    2. 6.1 Greatest Common Factor and Factor by Grouping
    3. 6.2 Factor Trinomials
    4. 6.3 Factor Special Products
    5. 6.4 General Strategy for Factoring Polynomials
    6. 6.5 Polynomial Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Rational Expressions and Functions
    1. Introduction
    2. 7.1 Multiply and Divide Rational Expressions
    3. 7.2 Add and Subtract Rational Expressions
    4. 7.3 Simplify Complex Rational Expressions
    5. 7.4 Solve Rational Equations
    6. 7.5 Solve Applications with Rational Equations
    7. 7.6 Solve Rational Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Roots and Radicals
    1. Introduction
    2. 8.1 Simplify Expressions with Roots
    3. 8.2 Simplify Radical Expressions
    4. 8.3 Simplify Rational Exponents
    5. 8.4 Add, Subtract, and Multiply Radical Expressions
    6. 8.5 Divide Radical Expressions
    7. 8.6 Solve Radical Equations
    8. 8.7 Use Radicals in Functions
    9. 8.8 Use the Complex Number System
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Quadratic Equations and Functions
    1. Introduction
    2. 9.1 Solve Quadratic Equations Using the Square Root Property
    3. 9.2 Solve Quadratic Equations by Completing the Square
    4. 9.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 9.4 Solve Quadratic Equations in Quadratic Form
    6. 9.5 Solve Applications of Quadratic Equations
    7. 9.6 Graph Quadratic Functions Using Properties
    8. 9.7 Graph Quadratic Functions Using Transformations
    9. 9.8 Solve Quadratic Inequalities
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Exponential and Logarithmic Functions
    1. Introduction
    2. 10.1 Finding Composite and Inverse Functions
    3. 10.2 Evaluate and Graph Exponential Functions
    4. 10.3 Evaluate and Graph Logarithmic Functions
    5. 10.4 Use the Properties of Logarithms
    6. 10.5 Solve Exponential and Logarithmic Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Conics
    1. Introduction
    2. 11.1 Distance and Midpoint Formulas; Circles
    3. 11.2 Parabolas
    4. 11.3 Ellipses
    5. 11.4 Hyperbolas
    6. 11.5 Solve Systems of Nonlinear Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  13. 12 Sequences, Series and Binomial Theorem
    1. Introduction
    2. 12.1 Sequences
    3. 12.2 Arithmetic Sequences
    4. 12.3 Geometric Sequences and Series
    5. 12.4 Binomial Theorem
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  14. 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
    11. Chapter 11
    12. Chapter 12
  15. Index

Review Exercises

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.

337.

12a2b3,15ab212a2b3,15ab2

338.

12m2n3,42m5n312m2n3,42m5n3

339.

15y3,21y2,30y15y3,21y2,30y

340.

45x3y2,15x4y,10x5y345x3y2,15x4y,10x5y3

Factor the Greatest Common Factor from a Polynomial

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

341.

35y+8435y+84

342.

6y2+12y66y2+12y6

343.

18x315x18x315x

344.

15m4+6m2n15m4+6m2n

345.

4x312x2+16x4x312x2+16x

346.

−3x+24−3x+24

347.

−3x3+27x212x−3x3+27x212x

348.

3x(x1)+5(x1)3x(x1)+5(x1)

Factor by Grouping

In the following exercises, factor by grouping.

349.

axay+bxbyaxay+bxby

350.

x2yxy2+2x2yx2yxy2+2x2y

351.

x2+7x3x21x2+7x3x21

352.

4x216x+3x124x216x+3x12

353.

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

354.

5x5yy+x5x5yy+x

Factor Trinomials

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

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

355.

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

356.

k216k+60k216k+60

357.

m2+3m54m2+3m54

358.

x23x10x23x10

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

359.

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

360.

r2+3rs28s2r2+3rs28s2

361.

a2+4ab21b2a2+4ab21b2

362.

p25pq36q2p25pq36q2

363.

m25mn+30n2m25mn+30n2

Factor Trinomials of the Form ax2+bx+cax2+bx+c Using Trial and Error

In the following exercises, factor completely using trial and error.

364.

x3+5x224xx3+5x224x

365.

3y321y2+30y3y321y2+30y

366.

5x4+10x375x25x4+10x375x2

367.

5y2+14y+95y2+14y+9

368.

8x2+25x+38x2+25x+3

369.

10y253y1110y253y11

370.

6p219pq+10q26p219pq+10q2

371.

−81a2+153a+18−81a2+153a+18

Factor Trinomials of the Form ax2+bx+cax2+bx+c using the ‘ac’ Method

In the following exercises, factor.

372.

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

373.

18a29a+118a29a+1

374.

15p2+2p815p2+2p8

375.

15x2+6x215x2+6x2

376.

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

377.

3x2+3x363x2+3x36

378.

48y2+12y3648y2+12y36

379.

18a257a2118a257a21

380.

3n412n396n23n412n396n2

Factor using substitution

In the following exercises, factor using substitution.

381.

x413x230x413x230

382.

(x3)25(x3)36(x3)25(x3)36

Factor Special Products

Factor Perfect Square Trinomials

In the following exercises, factor completely using the perfect square trinomials pattern.

383.

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

384.

36a284ab+49b236a284ab+49b2

385.

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

386.

5k370k2+245k5k370k2+245k

387.

75u430u3v+3u2v275u430u3v+3u2v2

Factor Differences of Squares

In the following exercises, factor completely using the difference of squares pattern, if possible.

388.

81r22581r225

389.

169m2n2169m2n2

390.

25p2125p21

391.

9121y29121y2

392.

20x212520x2125

393.

169n3n169n3n

394.

6p2q254p26p2q254p2

395.

24p2+5424p2+54

396.

49x281y249x281y2

397.

16z4116z41

398.

48m4n2243n248m4n2243n2

399.

a2+6a+99b2a2+6a+99b2

400.

x216x+64y2x216x+64y2

Factor Sums and Differences of Cubes

In the following exercises, factor completely using the sums and differences of cubes pattern, if possible.

401.

a3125a3125

402.

b3216b3216

403.

2m3+542m3+54

404.

81m3+381m3+3

General Strategy for Factoring Polynomials

Recognize and Use the Appropriate Method to Factor a Polynomial Completely

In the following exercises, factor completely.

405.

24x3+44x224x3+44x2

406.

24a49a324a49a3

407.

16n256mn+49m216n256mn+49m2

408.

6a225a96a225a9

409.

5u445u25u445u2

410.

n481n481

411.

64j2+22564j2+225

412.

5x2+5x605x2+5x60

413.

b364b364

414.

m3+125m3+125

415.

2b22bc+5cb5c22b22bc+5cb5c2

416.

48x5y2243xy248x5y2243xy2

417.

5q215q905q215q90

418.

4u5v+4u2v34u5v+4u2v3

419.

10m4625010m46250

420.

60x2y75xy+30y60x2y75xy+30y

421.

16x224xy+9y26416x224xy+9y264

Polynomial Equations

Use the Zero Product Property

In the following exercises, solve.

422.

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

423.

(5b+1)(6b+1)=0(5b+1)(6b+1)=0

424.

6m(12m5)=06m(12m5)=0

425.

(2x1)2=0(2x1)2=0

426.

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

Solve Quadratic Equations by Factoring

In the following exercises, solve.

427.

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

428.

y2y72=0y2y72=0

429.

2p211p=402p211p=40

430.

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

431.

144m225=0144m225=0

432.

4n2=364n2=36

433.

(x+6)(x3)=−8(x+6)(x3)=−8

434.

(3x2)(x+4)=12x(3x2)(x+4)=12x

435.

16p3=24p29p16p3=24p29p

436.

2y3+2y2=12y2y3+2y2=12y

Solve Equations with Polynomial Functions

In the following exercises, solve.

437.

For the function, f(x)=x2+11x+20,f(x)=x2+11x+20, find when f(x)=−8f(x)=−8 Use this information to find two points that lie on the graph of the function.

438.

For the function, f(x)=9x218x+5,f(x)=9x218x+5, find when f(x)=−3f(x)=−3 Use this information to find two points that lie on the graph of the function.

In each function, find: the zeros of the function the x-intercepts of the graph of the function the y-intercept of the graph of the function.

439.

f(x)=64x249f(x)=64x249

440.

f(x)=6x213x5f(x)=6x213x5

Solve Applications Modeled by Quadratic Equations

In the following exercises, solve.

441.

The product of two consecutive odd numbers is 399. Find the numbers.

442.

The area of a rectangular shaped patio 432 square feet. The length of the patio is 6 feet more than its width. Find the length and width.

443.

A ladder leans against the wall of a building. The length of the ladder is 9 feet longer than the distance of the bottom of the ladder from the building. The distance of the top of the ladder reaches up the side of the building is 7 feet longer than the distance of the bottom of the ladder from the building. Find the lengths of all three sides of the triangle formed by the ladder leaning against the building.

444.

Shruti is going to throw a ball from the top of a cliff. When she throws the ball from 80 feet above the ground, the function h(t)=−16t2+64t+80h(t)=−16t2+64t+80 models the height, h, of the ball above the ground as a function of time, t. Find: the zeros of this function which tells us when the ball will hit the ground. the time(s) the ball will be 80 feet above the ground. the height the ball will be at t=2t=2 seconds which is when the ball will be at its highest point.

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