copyright © 2010 pearson education, inc. all rights reserved. 6.5 – slide 1


Factoring and Applications

Chapter 6


6.5

Special Factoring Techniques


6.5 Special Factoring Techniques

Objectives

1. Factor a difference of squares.

2. Factor a perfect square trinomial.

3. Factor a difference of cubes.

4. Factor a sum of cubes.


Factor a difference of squares




Example 1 Factor each binomial, if possible.


(a) x2 49

(b) y2 m2 = (y – m)(y + m)

(continued)



Example 1 Factor each binomial, if possible.


(d) x2 8

(e) p2 + 16

It is a prime polynomial because 8 is not the square of an integer.

It is a prime polynomial since it is a sum of squares.



Example 2 Factor each difference of squares.




Example 3 Factor completely.



Factor a perfect square trinomial.




Example 4 Factor x2 + 10x + 25.


The term x2 is a perfect square, and so is 25. Try factoring as (x + 5)2.To check, take twice the product of the two terms in the squared binomial.

Since 10x is the middle term of the trinomial, the trinomial is a perfect square and can be factored as (x + 5)2.



Example 5 Factor each trinomial.


(a) x2 – 22x + 121The first and last terms are perfect squares.Check to see if the middle term is twice the product of

the first and last terms of the binomial x – 11.





Twice the product of the first and last terms is 2(5y)4 = 40y, which is not the middle term.The trinomial is not a perfect square. It is a prime polynomial.



Factor a difference of cubes.



Example 6a Factor the difference of cubes.




Example 6c Factor the difference of cubes.




Factor a sum of cubes.



Example 7a Factor the sum of cubes.




Example 7b Factor the sum of cubes.


copyright © 2010 pearson education, inc. all rights reserved. 6.5 – slide 1

Documents

factor x

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pearson education

perfect square trinomial

perfect squares

difference of squares

binomial x

term x