Bell Ringer:

1. Homework: Textbook- Read 518-520 Do: P. 520 -558: 2,3,4,5,8,14,22,28 , 34 Objective: SWBAT: factor trinomials of the form ax2 + bx + c Bell Ringer: You are making square shaped invitations for a party. You start with a square piece of paper with 6-in sides. You reduce both its length and its width by x. What is the area of the invitation? Justify our reasoning. • 5 minutes • 4 minutes • 3 minutes • 2 minutes • 1 minute • 30 seconds • TIMES UP!!!

2. Homework: Textbook- Read 518-520 Do: P. 520 -558: 2,3,4,5,8,14,22,28 , 34 Objective: SWBAT: factor trinomials of the form ax2 + bx + c Bell Ringer: You are making square shaped invitations for a party. You start with a square piece of paper with 6-in sides. You reduce both its length and its width by x. What is the area of the invitation? Justify our reasoning. Answer: Width is (60-x) in and length is (60-x) in. So the area is (6-x)2. This equals 36-12x+xs

3. Homework: Textbook- Read 518-520 Do: P. 520 -558: 2,3,4,5,8,14,22,28 , 34 Objective: SWBAT: factor trinomials of the form ax2 + bx + c Some trinomials of the form ax2 + bx + c can be written as the product of binomials 6x2 + 23x + 7 look for factors of the product ac where that sum to be b So, 23x =2x + 21x substitute 6x2 + 23x + 7 ax2 + bx + c = 6x2 + 2x + 21x + 7 Next, get the GCF for each pair of terms 6x2 & 2x : 2x 21x + 7: 7 So, 2x (3x + 1) + 7(3x + 1) Or (2x+7)(3x+1)

4. Homework: Textbook- Read 518-520 Do: P. 520 -558: 2,3,4,5,8,14,22,28 , 34 Objective: SWBAT: factor trinomials of the form ax2 + bx + c Example #2 6x2+ 13x + 5 1. The factors of ac that have the sum of b: ac = 30 and b = 13 Factors of 30: 10, 3 15,2 6,5 Sum of factors: 13 17 11 ax2 + bx + c 2. Use factor to rewrite bx = 6x2 +3x + 10x + 5 =3x(x+1) + 5(2x +1) factor out GCF

5. Homework: Textbook- Read 518-520 Do: P. 520 -558: 2,3,4,5,8,14,22,28 , 34 Objective: SWBAT: factor trinomials of the form ax2 + bx + c Prior example shows when ac is positive Factoring when ac is negative: Step 1: ac = -140, so find factors of ac with a sum of be… where b is 31. Step 2: Factors of -140 -14, 10 -10, 15 -7, 20 -20, 7 -4,35 4, -35 10x2 + 31x -14 -4, 35.. so 31x = -4x + 35x ax2 + bx + c 10x2 + 31x -14 =10x2 -4x + 35x -14 = 2x(5x -2) +7(5x-2) factor out gcf = (2x +7)(5x -2) dist property

6. Homework: Textbook- Read 518-520 Do: P. 520 -558: 2,3,4,5,8,14,22,28 , 34 Objective: SWBAT: factor trinomials of the form ax2 + bx + c The area of a rectangle is 8x2 + 22x + 15. What are the possible dimensions of the rectangle? Problem: ac = 120 b = 22 Factors: 20, 6 2, 60 4, 30 40, 3 12,10 Thus 22x = 12x + 10x 8x2 + 22x + 15 = 8x2 + 12x + 10x + 15 =4x(2x +3) + 5(2x +3) =(4x+5)(2x+3)

7. Homework: Textbook- Read 518-520 Do: P. 520 -558: 2,3,4,5,8,14,22,28 , 34 Objective: SWBAT: factor trinomials of the form ax2 + bx + c 8x2 -36x – 20 Sometimes it may be necessary to factor out a monomial and then factor the remaining polynomial into binomials: = 4(2x2 - 9x - 5) = 4(2x2 + 10x - 1x - 5) = 4(2x(x + 5) - (x+5)) = 4(2x-1)(x+5)

8. Homework: Textbook- Read 518-520 Do: P. 520 -558: 2,3,4,5,8,14,22,28 , 34 Objective: SWBAT: factor trinomials of the form ax2 + bx + c Table/Group Problem Be prepared to present to the class. A cylinder had a radius of x+1 and a height of x+4. Write a polynomial in standard for that best describes the total surface area of the cylinder.

9. Homework: Textbook- Read 518-520 Do: P. 520 -558: 2,3,4,5,8,14,22,28 , 34 Objective: SWBAT: factor trinomials of the form ax2 + bx + c Reflection Describe the relationship between ac and b in ax2 + bx + c