1. Warm-Up #2 Multiply these polynomials. 1) (x-5) 2 2) (8x-1) 2 3. (4x- 3y)(3x +4y) Homework: P5 (1,3,5,11,13,17,27,33,41, 45,49,55,59,63,71,73,77) Answers: 1) x 2 – 10x + 25 2) 64x 2 – 16x + 1 3) 12x 2 y 2 + 7xy - 12y 2

2. What are at least 3 ways to factor polynomials? Daily Question

3. Announcements: Quiz P4/P5 on 7/26!!! Section P5: Factoring Polynomials Factoring GCF, Trinomials, By grouping, Difference of Two Squares Sum or Difference of a cube

4. Factoring GCF Ex1: 16x – 24 Ex 2: 6x 4 -12x 3 + 12x 2 8(2x – 3) 6x 2 (x 2 – 2x + 2) YOU TRY: 12x 5 – 8x 4 + 4x 2 4x 2 (3x 3 – 2x 2 + 1)

5. Factoring Perfect Trinomials Ex 3: x 2 +12x +36 (x +6)(x+6) (x+6) 2 Ex. 4: 25x 2 -60x + 36 (5x-6) (5x-6) (5x-6) 2 * (a+b) 2 or (a-b) 2

6. Factoring Trinomials – Don’t forget GCF! x 2 + x - 12 2x 2 – 11x – 6 6x 2 + 14x + 8 (x + 4)(x – 3) (2x + 1)(x – 6) 2(3x + 4)(x+1)

7. YOU TRY: 3x 2 -2x -5 6x 2 -18x-60 (3x-5)(x+1) 6(x-5)(x+2)

8. Factoring by Grouping Ex. 5: x 3 - 2x 2 + 5x -10 Ex. 6: x 3 - 3x 2 + 4x -12 3x 3 - 2x 2 - 6x + 4 YOU TRY: (x-2)(x 2 +5) (x-3)(x 2 +4) (3x-2)(x 2 -2)

9. Factoring the Difference of Two Squares Ex. 7: x 2 -4 * Remember to take the square root of the 1 st term and the last term. One factor is positive and one factor is negative. (x+2)(x-2) Ex.8: 81x 2 - 49 (9x-7)(9x+7)

10. YOU TRY: 36x 2 -49y 2 (6x-7y)(6x+7y)

11. Factoring the Sum and Difference of Cubes: Don’t forget to check for the GCF!! Formulas: SUM: A 3 + B 3 = (A + B)(A 2 – AB + B 2 ) DIFFERENCE: A 3 - B 3 = (A-B)(A 2 + AB + B 2 ) A and B come from cube rooting the terms in the problem.

12. Example 9: a) x 3 + 8 Step 1: Check for GCF, there is none Step 2: Cube root terms A = x and B = 2 Step 3: Follow formula A 3 + B 3 = (A + B)(A 2 – AB + B 2 ) = (x+ 2)(x 2 - 2x + 4)

13. Example 10: b) 64x 3 -125 Step 1: Check for GCF, there is none Step 2: Cube root terms A = 4x and B = 5 Step 3: Follow formula A 3 - B 3 = (A - B)(A 2 + AB + B 2 ) = (4x - 5)(16x 2 + 20x + 25)

14. YOU TRY!!! a) x 3 + 64b) 125x 3 – 8 Answers: a) (x+4)(x 2 – 4x + 16) b) (5x – 2)(25x 2 + 10x + 4)

15. Summary: Which type of factoring a polynomial do you like the best and why? Which type of factoring a polynomial do you think is the hardest for you and why?