1. College Algebra K/DC Friday, 26 September 2014 OBJECTIVE TSW factor using (1) the pattern of difference of two squares, and (2) the pattern of the sum and difference of two cubes. ASSIGNMENTS DUE TODAY –Sec. R.4: pp. 40-41 (1-16 all, 18-23 all)  wire basket –Sec. R.4: p. 41 (51-60 all + my problems)  black tray (will be done in class today) ASSIGNMENT DUE MONDAY –Sec. R.4: p. 41 (25-45 odd) QUIZ ON MONDAY –Factoring polynomials by GCF, Grouping, and Trinomials

2. R-2 Factoring Polynomials R.4 Factoring Binomials – Differences of Squares

3. Factoring Differences of Squares REMEMBER: When factoring, ALWAYS look for a GCF 1 st. Then, look for a pattern: 1.Are there four terms? If it factors, you’ll probably use grouping. 2.Are there three terms? If it factors, you’ll probably factor using guess and check or the box method. R-3

4. Factoring Differences of Squares 3.Are there two terms? If there are, is the problem a difference (subtraction)? a.Are the two terms perfect squares? If they are, then use the pattern of differences of squares. R-4

5. Factoring Differences of Squares If there is a GCF, factor it out first: Be careful: R-5

6. R-6 Example Factoring Differences of Squares Factor each binomial: (a) (b) (c)

7. R-7 Example Factoring Differences of Squares Sometimes, you may have to factor more than once. Always factor completely (factor until you can’t factor anymore)!

8. College Algebra K/DC Tuesday, 29 September 2015 OBJECTIVE TSW factor using the pattern of the sum and difference of two cubes. ASSIGNMENT DUE –Sec. R.4: pp. 38-39 (25-45 odd, 51-60 all)  wire basket ASSIGNMENT DUE TOMORROW/THURSDAY –Sec. R.4: pp. 39-40 (61-70 all, 93, 95)  today’s assignment ASSESSMENT TOMORROW/THURSDAY –Polynomials Partners (I choose) –Thursday: 6 th Period Only – ‘C’ Lunch!!! TEST ON TUESDAY, 10/07/2015 –Factoring

9. Factoring Polynomials R.4 Factoring Sums and Differences of Cubes

10. Sums or Differences of Cubes The key is to recognize that the two terms are perfect cubes and then determine their cube roots. Perfect CubeCube Root

11. Sums or Differences of Cubes Recall the pattern for factoring a difference of squares: The pattern for factoring a difference (subtraction) of cubes is similar: If the expression is a sum (addition):

12. Sums or Differences of Cubes To remember the signs, just use SOAP: Same Opposite Always Positive

13. Example Factoring Sums or Differences of Cubes Factor each polynomial: (a) (b)

14. Example Factoring Sums or Differences of Cubes Factor each polynomial: (c)

15. Example Factoring Sums or Differences of Cubes Factor each polynomial: (d) prime

16. R-16 Assignment: Sec. R.4: pp. 39-40 (61-70 all, 93, 95) Write the problem and factor each polynomial.