Bell Ringer: 5 minutes 4 minutes 3 minutes 2 minutes 1 minute 30 seconds TIMES UP!!! 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. Objective: SWBAT: factor trinomials of the form ax 2 + bx + c Homework: Textbook- Read Do: P : 2,3,4,5,8,14,22,28, 34

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+x s Objective: SWBAT: factor trinomials of the form ax 2 + bx + c Homework: Textbook- Read Do: P : 2,3,4,5,8,14,22,28, 34

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

Example #2 6x x 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: Use factor to rewrite bx = 6x 2 +3x + 10x + 5 =3x(x+1) + 5(2x +1) factor out GCF ax 2 + bx + c Objective: SWBAT: factor trinomials of the form ax 2 + bx + c Homework: Textbook- Read Do: P : 2,3,4,5,8,14,22,28, 34

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 x x -14 Step 2: Factors of , , 15 -7, , 7 -4,35 4, -35 ax 2 + bx + c -4, 35.. so31x = -4x + 35x 10x x -14 =10x 2 -4x + 35x -14 = 2x(5x -2) +7(5x-2) factor out gcf = (2x +7)(5x -2) dist property Objective: SWBAT: factor trinomials of the form ax 2 + bx + c Homework: Textbook- Read Do: P : 2,3,4,5,8,14,22,28, 34

Objective: SWBAT: factor trinomials of the form ax 2 + bx + c Homework: Textbook- Read Do: P : 2,3,4,5,8,14,22,28, 34 The area of a rectangle is 8x x 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 8x x + 15 = 8x x + 10x + 15 =4x(2x +3) + 5(2x +3) =(4x+5)(2x+3)

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

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. Homework: Textbook- Read Do: P : 2,3,4,5,8,14,22,28, 34 Objective: SWBAT: factor trinomials of the form ax 2 + bx + c

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