1. Table of Contents Factoring – Review of Basic Factoring The following is a quick review of basic factoring 1.Common Factor Example 1:

2. Table of Contents 2.Difference of two squares Pattern: Example 2:

3. Table of Contents 3.Sum of two squares Pattern: A sum of two squares cannot be factored. Example 3: Try to factor the following:

4. Table of Contents We can’t find two factors that multiply to give us the sum of two squares,

5. Table of Contents 4.Difference of two cubes Pattern: Example 4:

6. Table of Contents 5.Sum of two cubes Pattern: Example 5:

7. Table of Contents 6.Perfect square trinomial Pattern:

8. Table of Contents Example 6: Perfect square trinomial What do you square to get the first term of x squared? What do you square to get the last term of 36? Find the product of these two terms and then double it.

9. Table of Contents Since the result of 12x is the same as the middle term … … the trinomial is a perfect square trinomial. Take the binomial … and insert a plus sign (same sign as the middle term) Square the binomial and the trinomial is factored.

10. Table of Contents Example 7: Perfect square trinomial What do you square to get the first term of x squared? What do you square to get the last term of 9? Find the product of these two terms and then double it.

11. Table of Contents Since the result of 6x is the same as the middle term … … the trinomial is a perfect square trinomial. Take the binomial … and insert a negative sign (same sign as the middle term) Square the binomial and the trinomial is factored.

12. Table of Contents 7.Trinomial There are two methods for factoring a trinomial, guess and check, and the ac method. The guess and check method will be reviewed here. See the authors website for help with the ac method.

13. Table of Contents Example 8: Trinomial Write two binomials. The product of the first terms of the binomials must equal the first term of the trinomial. Since the third term of the trinomial is negative, the signs must be opposite.

14. Table of Contents Consider the possible factors of the third term, 6.

15. Table of Contents Try the different pairs of factors in the binomial, and see if the outside and inside matches the middle term. No Yes

16. Table of Contents The correct factorization of the trinomial is … Remember that if the outside and inside yields the right numerical value, but opposite in sign, simply switch the two signs and the trinomial is factored.

17. Table of Contents Example 9: Trinomial Write two binomials. The product of the first terms of the binomials must equal the first term of the trinomial. Since the value of a is not 1 in this case, we must consider the possible factorizations of 6.

18. Table of Contents Try 1 and 6 along with the values of x to get the first term. Since the third term of the trinomial is positive, the signs must be the same. Since the middle term of the trinomial is negative, the signs are both negative.

19. Table of Contents Consider the possible factorizations of the third term. We now have a number of possibilities to try. For the leading term we have … and for the last term we have …

20. Table of Contents Try the first combination, and see if the outside and inside matches the middle term. No

21. Table of Contents Since the leading coefficient was not 1, we need to turn around the last term’s values and try again. No

22. Table of Contents Note that we did get a different value than the first time, but it still does not match the middle term of the trinomial. No

23. Table of Contents Try the other pair of factors of the first term, with the same pair of factors for the last term. No

24. Table of Contents Once again, turn around the last pair. Yes

25. Table of Contents The factorization of the trinomial is given by …

26. Table of Contents 8.Grouping method Consider the grouping method when there are four terms. Example 10: Group the polynomial into two binomials.

27. Table of Contents Factor each binomial. Factor out the common binomial factor

28. Table of Contents