1. You need:textbookApril 7, 2009 calculator *Turn in Math March Madness! HW answers: p.607 13. B25. (x – 15)(x – 30) 16. (t – 3)(t – 7)29. (x -2)(x – 7) 19. (y – 6)(y + 3)roots = 2 and 7 22. (4 + n)(8 + n)34. (x + 7)(x – 8) roots = -7 and 8 41. (x – 2)(x – 9) roots = 2 and 9

2. 10.6 Factoring ax2 + bx + c (where a ≠ 1) In this section, all of the trinomials will have either a positive or negative leading coefficient. The textbook has a method that works based on guess and check – look at page 611 right now. Now look at page 612. It sometimes makes you do a lot of work!

3. My way to solve ax 2 + bx + c is called SLIDE and DIVIDE To factor the problem in Example #3 (p.612), 6x 2 – 19x + 15 First SLIDE - slide the leading coefficient over to the c term and multiply. 6X 2 – 19x + (15 * 6)

4. Your newly created trinomial looks like: x 2 – 19x + 90 Now you can factor the trinomial like yesterday (find two numbers that multiply to equal 90m, but also add up to -19). Factors of 90: 1, 902, 453, 305,186, 15 9, 10-1,-90-2,-45-3,-30-5,-18 -6,-15-9,-10 Which number add up to -19?

5. You hopefully picked -9 and -10 so (x – 9) (x – 10) Second, DIVIDE – place the original leading coefficient (6) under the numbers you chose (like the 6 is dividing): (x – 9) (x – 10) 6 6 Now, simplify each fraction: (x – 3) (x – 5) 2 3

6. You’re almost done! Since neither fraction simplified to a whole number, MOVE the denominator in front of each x : (x – 3) (x – 5) 2 3 (2x – 3) (3x – 5) This is your factored form of 6x 2 – 19x + 15. CHECK Use FOIL or Dist.Prop. to see if you get the original trinomial back.

7. Here’s another example of Slide and Divide: Factor 2x 2 + 7x + 6. SLIDE 1.Slide the lead. coeff. (2) over to the c (6) and multiply. X 2 + 7x + (2 * 6) X 2 + 7x + 12 2. Now factor the trinomial (find 2 numbers that mult. to 12 and add up to 7)

8. You now have (x + 3) (x + 4) [or the reverse] DIVIDE 1. Place the original lead. coeff. under each number in the ( ). (x + 3) (x + 4) 2 2 2. Now simplify each fraction. (x + 3) (x + 2) 2

9. Because the 3/2 didn’t simplify to a whole number, MOVE the 2 up in front of the x: (2x + 3) (x + 2) CHECK by FOIL or Dist. Prop. Now find the roots – set each ( ) equal to zero (2x + 3) = 0(x + 2) = 0 2x + 3 = 0x + 2 = 0 x = -3/2 x = -2 The roots to the parabola 2x 2 + 7x +6 are -3/2 and -2.

10. Confused again? Get someone to help you who understands how to Slide and Divide. Practice: p.614, #5-8 matching Homework: p.614, #17, 21, 23, 24, 28, 30, 31