1. Section P5 Factoring Polynomials

2. Common Factors

3. Factoring a polynomial containing the sum of monomials
mean finding an equivalent expression that is a product.
In this section we will be factoring over the set of integers,
meaning that the coefficients in the factors are integers.
Polynomials that cannot be factored using integer
coefficients are called prime.

4. Example
Factor:

5. Factoring by Grouping

6. Sometimes all of the terms of a polynomial may not
contain a common factor. However, by a suitable
grouping of terms it may be possible to factor. This
is called factoring by grouping.

7. Example
Factor by Grouping:

8. Example
Factor by Grouping:

9. Factoring Trinomials

11. + + Factors of 8 8,1 4,2 -8,-1 -4,-2 Sum of Factors 9 6 -9 -6 4 2
Choose either two positive or two negative factors since the sign in front of the 8 is positive.

12. - + 1 5 Factor: Possible factorizations
Sum of outside and inside products 1 5
Since the sign in front of the 5 is a negative, one factor will be positive and one will be negative.

13. Possible Factorizations Sum of Inside and Outside products
Example
Factor:
Possible Factorizations
Sum of Inside and Outside products

14. Example Factor: Possible Factorizations
Sum of Inside and outside Products

15. Factoring the Difference of Two Squares

18. Repeated Factorization- Another example
Can the sum of two squares be factored?

19. Example
Factor Completely:

20. Example
Factor Completely:

21. Example
Factor Completely:

22. Factoring Perfect Square Trinomials

24. Example
Factor:

25. Example
Factor:

26. Factoring the Sum and Difference of Two Cubes

28. Example
Factor:

29. Example
Factor:

30. Example
Factor:

31. A Strategy for Factoring Polynomials

33. Example
Factor Completely:

34. Example
Factor Completely:

35. Example
Factor Completely:

36. Example
Factor Completely:

37. Example
Factor Completely:

38. Example
Factor Completely:

39. Factoring Algebraic Expressions Containing Fractional and Negative Exponents

40. Expressions with fractional and negative exponents are not polynomials, but they can be factored using similar techniques. Find the greatest common factor with the smallest exponent in the terms.

41. Example
Factor and simplify:

42. Example
Factor and simplify:

43. Example
Factor and simplify:

44. Factor Completely:
(a)
(b)
(c)
(d)

45. Factor Completely:
(a)
(b)
(c)
(d)