Prentice Hall Algebra 2

Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Divide using long division. Check your answers.

  1. open , x squared , minus 3 x minus 40 close divides open x plus 5 close
  2. open 3 , x squared , plus 7 x minus 20 close divides open x plus 4 close
  3. open , x cubed , plus , 3 x squared , minus x plus 2 close divides open x minus 1 close
  4. open 2 , x cubed , minus , 3 x squared , minus 18 x minus 8 close divides open x minus 4 close
  5. open 3 , x cubed , plus , 9 x squared , plus 8 x plus 4 close divides open x plus 2 close
  6. open 9 , x squared , minus 21 x minus 20 close divides open x minus 1 close
  7. open , x squared , minus 7 x plus 10 close divides open x plus 3 close
  8. open , x cubed , minus 13 x minus 12 close divides open x minus 4 close

See Problem 2.

Determine whether each binomial is a factor of x cubed , plus 4 , x squared , plus x minus 6 .

  1. x plus 1
  2. x plus 2
  3. x plus 3
  4. x minus , 3

See Problem 3.

Divide using synthetic division.

  1. open , x cubed , plus , 3 x squared , minus x minus 3 close divides open x minus 1 close
  2. open , x cubed , minus , 4 x squared , plus 6 x minus 4 close divides open x minus 2 close
  3. open , x cubed , minus , 7 x squared , minus 7 x plus 20 close divides open x plus 4 close
  4. open , x cubed , minus , 3 x squared , minus 5 x minus 25 close divides open x minus 5 close
  5. open , x squared , plus 3 close divides open x minus 1 close
  6. open 3 , x cubed , plus , 17 x squared , plus 21 x minus 9 close divides open x plus 3 close
  7. open , x cubed , plus 27 close divides open x plus 3 close
  8. open 6 , x squared , minus 8 x minus 2 close divides open x minus 1 close

See Problem 4.

Use synthetic division and the given factor to completely factor each polynomial function.

  1. y equals , x cubed , plus 2 , x squared , minus 5 x minus 6 semicolon open x plus 1 close
  2. y equals , x cubed , minus , 4 x squared , minus 9 x plus 36 semicolon open x plus 3 close
  3. Geometry The volume, in cubic inches, of the decorative box shown can be expressed as the product of the lengths of its sides as v open x close equals , x cubed , plus , x squared , minus 6 x .  What linear expressions with integer coefficients represent the length and height of the box?

    A box is x long.


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Table of Contents

Prentice Hall Algebra 2 Chapter 1 Expressions, Equations, and Inequalities Chapter 2 Functions, Equations, and Graphs Chapter 3 Linear Systems Chapter 4 Quadratic Functions and Equations Chapter 5 Polynomials and Polynomial Functions Chapter 6 Radical Functions and Rational Exponents Chapter 7 Exponential and Logarithmic Functions Chapter 8 Rational Functions Chapter 9 Sequences and Series Chapter 10 Quadratic Relations and Conic Sections Chapter 11 Probability and Statistics Chapter 12 Matrices Chapter 13 Periodic Functions and Trigonometry Chapter 14 Trigonometric Identities and Equations Skills Handbook English/Spanish Illustrated Glossary Selected Answers Index Acknowledgments