1. Copyright © 2007 Pearson Education, Inc. Slide R-1

2. Copyright © 2007 Pearson Education, Inc. Slide R-2 Chapter R: Reference: Basic Algebraic Concepts R.1Review of Exponents and Polynomials R.2Review of Factoring R.3Review of Rational Expressions R.4Review of Negative and Rational Exponents R.5Review of Radicals

3. Copyright © 2007 Pearson Education, Inc. Slide R-3 R.2 Review of Factoring Factoring is the process of finding polynomials, called factors, whose product equals a given polynomial. A polynomial that cannot be written as a product of polynomials with integer coefficients is a prime or irreducible polynomial. A polynomial is factored completely when it is written as a product of prime polynomials with integer coefficients.

4. Copyright © 2007 Pearson Education, Inc. Slide R-4 R.2 Factoring Out the Greatest Common Factor Example Factor out the greatest common factor. (a)(b) Solution (a) (b)

5. Copyright © 2007 Pearson Education, Inc. Slide R-5 R.2 Factoring by Grouping Example Factor each polynomial by grouping. (a)(b) Solution (a)

6. Copyright © 2007 Pearson Education, Inc. Slide R-6 R.2 Factoring by Grouping Solution (b)

7. Copyright © 2007 Pearson Education, Inc. Slide R-7 R.2 Factoring Trinomials Example Factor each trinomial. (a) (b)

8. Copyright © 2007 Pearson Education, Inc. Slide R-8 R.2 Factoring Trinomials Solution (a) We must find integers a, b, c, d such that By FOIL, we see that ac = 4 and bd = 6. Thus a and c are 1 and 4 or 2 and 2. Since the middle term is negative, consider only negative values for b and d. The possibilities are –1 and –6 or –2 and –3.

9. Copyright © 2007 Pearson Education, Inc. Slide R-9 R.2 Factoring Trinomials Solution (a) Try these combinations of factors The last trial gives the correct factorization.

10. Copyright © 2007 Pearson Education, Inc. Slide R-10 R.2 Factoring Trinomials Solution (b) Try the various combinations of factors The last trial gives the correct factorization.

11. Copyright © 2007 Pearson Education, Inc. Slide R-11 R.2 Factoring Special Products Perfect Square Trinomials

12. Copyright © 2007 Pearson Education, Inc. Slide R-12 R.2 Factoring Perfect Square Trinomials Example Factor each polynomial. (a)(b) Solution (a) (b)

13. Copyright © 2007 Pearson Education, Inc. Slide R-13 R.2 Factoring Special Products Difference of Squares

14. Copyright © 2007 Pearson Education, Inc. Slide R-14 R.2 Factoring Differences of Squares Example Factor each polynomial. (a)(b) Solution (a) (b)

15. Copyright © 2007 Pearson Education, Inc. Slide R-15 R.2 Factoring Special Products Difference and Sums of Cubes Difference of cubes Sum of cubes

16. Copyright © 2007 Pearson Education, Inc. Slide R-16 R.2 Factoring Sums and Differences of Cubes Example Factor each polynomial. (a)(b) Solution (a)

17. Copyright © 2007 Pearson Education, Inc. Slide R-17 R.2 Factoring Sums and Differences of Cubes Solution (b)

18. Copyright © 2007 Pearson Education, Inc. Slide R-18 R.2 Factoring by Substitution Example Factor the polynomial Solution Replacing 2a – 1 with m and factoring gives Now, replace m with 2a – 1 in the factored form and simplify.

19. Copyright © 2007 Pearson Education, Inc. Slide R-19 R.2 Factoring by Substitution Solution