1. Factoring Expectation: A1.1.3: Factor algebraic expressions.

2. Common Factors The first thing to look for in any factoring situation is a common factor among all of the terms of the polynomial. ex: 4x 3 + 8x 2 – 16x + 32

3. Product/Sum If x 2 + bx + c factors neatly, it factors into (x+d)(x+e) where d + e = b and de = c.

4. Factor the following: x 2 + 8x + 15 x 2 – 7x + 12 x 2 + 10x - 11

5. Factor the following: x 2 – 4x - 21 x 2 + x - 132 x 2 + 34x - 72

6. Factor the following: x 2 – 49 3x 2 - 3x - 90 3x 3 – 6x 2 – 2x

7. Difference of Squares a 2 – b 2 = (a + b)(a – b) ex: x 2 – 36 = (x + 6)(x – 6) 4x 2 – 100 = (2x + 10)(2x – 10)

8. Sum of Squares The sum of 2 perfect squares does not factor. x 2 + 36 is prime 10x 2 + 144 is prime

9. Factor the Following x 2 – 64 27x 2 - 147

10. Completing the Square Sometimes it is helpful to modify a trinomial that is not factorable, so that we can factor it. Finding centers and the radius of a circle or the vertex and symmetry line for a parabola are 2 such situations. Completing the square allows us to do that.

11. Completing the Square 1. Group the x 2 and x terms in a quantity (x 2 + bx). 2. Add ( b / 2 ) 2 inside the quantity and subtract it outside. 3. x 2 + bx + ( b / 2 ) 2 factors into (x + ( b / 2 )) 2

12. Factor by completing the square. x 2 – 6x + 21

13. Factor by completing the square. x 2 + 8x - 20

14. Factor by completing the square. x 2 + 12x - 10

15. Factor by completing the square. x 2 –12x - 13

16. Factor by completing the square. x 2 – 5x - 4

17. Solve x 2 + 6x = 47 by completing the square.

18. What is the center and radius of the circle with equation x 2 – 4x + y 2 + 10y = 0