1. Sec. P.4
Factoring

2. Factoring Process of writing a polynomial as a product
Used to solve equations and reduce fractional expressions

3. Prime Polynomial that cannot be factored using integer coefficients
(Also said to be irreducible over the integers)

4. x2 - 3
Irreducible over the integers

5. Completely Factored
When each of its factors are prime

6. The simplest type is reversing the distributive property
a(b + c) = ab + ac distributive property
Reverse
ab + ac = a(b + c) a is the common factor

7. “Factoring Out” common factors is the 1st step in factoring polynomials

8. EX 1
6x3 – 4x
b) (x – 2)(2x) + (x – 2)(3)

9. Factoring special polynomial forms
Difference of 2 squares
u2 – v2 = (u + v)(u – v)

10. EX
(x2 – 9)
c) (x + 3)2 – y2
b) 4x2 – 9
d) y6 – z4

11. Sometimes you may need to remove a common factor before you can factor more.
EX 2
3 – 12x2

12. EX 3
a) (x + 2)2 – y2
b) 16x4 - 81

13. Perfect Square Trinomials
u2 + 2uv + v2 = (u + v)2
U2 – 2uv + v2 = (u – v)2

14. EX
a) x2 + 6x + 9
b) x2 – 6x + 9

15. Ex. 4
a) 16x2 + 8x + 1
b) x2 – 10x + 25

16. Try these
4x x + 25
x2 - 8x + 16
y6 – 12y3 + 36

17. Sum or Difference of two cubes
u3 + v3 = (u + v)(u2 – uv + v2)
u3 – v3 = (u – v)(u2 + uv + v2)

18. EX
a) x3 + 8
b) 27x3 - 1

19. EX 5
a) x3 - 27
b) 3(x3 + 64)

20. Try
x3 – 125
x6 – y12
8x3 – 1
27a6 + b9