Warm-up Dec. 13Good morning! Please get started on the Factor It! worksheet. You will be working with your shoulder partners. One person will work on the odd number questions and the other will work on the even number questions. You have 15 minutes.

Take out your hw. For those who were absent from class yesterday, please make sure you see me during lunch to make up your quiz.

HW 17: red text p. 236 #s 9, 11, 14, 15 and Factor It worksheet Study for your test

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Factor It!

1. Find three positive consecutive integers such that the product of the first and second is 2 more than 9 times the third.

x(x + 1) = 9(x + 2) + 2 x2 + x = 9x + 18 + 2 x2 + x = 9x + 20 -20 -9x -9x -20 x2 – 8x – 20 = 0 (x + 2)(x – 10) = 0x + 2 = 0 x – 10 = 0 -2 -2 +10 +10 x = -2 x = 10

Answer: 10, 11, & 12

Let x = 1st CPI x + 1 = 2nd CPI x + 2 = 3rd CPI

2. The length of a rectangle is 1 foot more than twice the width.  The area is 55 square feet.  Find the dimensions of the rectangle.

Let width = x length = 2x + 1 2(5) + 1 = 11

A = lw 55 = x(2x + 1) 55 = 2x2 + x -55 -55 0 = 2x2 + x – 55 0 = 2x2 – 10x + 11x – 55 0 = 2x(x – 5) + 11(x – 5) 0 = (2x + 11)(x – 5) 0 = 2x + 11 x – 5 = 0-11 -11 +5 +5-11 = 2x x = 5 2 2

Answer: The width is 5 feet and the length is 11 feet.

3. The length of a rectangular solid is 7. The width of the solid is 2 more than the height. The volume of the solid is 105. Find the width and the height of the solid.

Let height = x width = x + 2 length = 7

3 + 2 = 5

V = lwh 105 = 7(x + 2)(x) 105 = 7(x2 +2x) 105 = 7x2 + 14x -105 -105 0 = 7x2 + 14x – 105 0 = 7(x2 + 2x – 15) 0 = 7(x + 5)(x – 3) 0 = x + 5 x – 3 = 0-5 -5 +3 +3-5 = x x = 3

Answer: The height is 3 feet and the width is 5 feet.

4. The width of a rectangle is 12 less than its length. The area is 45 square inches. Find the dimensions of the rectangle.

Let length = x width = x – 12

A = lw 45 = x (x – 12) 45 = x2 – 12x -45 -45 0 = x2 – 12x – 45 0 = (x + 3)(x – 15 ) 0 = x + 3 x – 15 = 0-3 -3 +15 +15-3 = x x = 15

Answer: The length is 15 feet and the width is 3 feet.

5. What is the largest of three consecutive odd integers if the product of the first and third integers is 6 more than three times the second integer?

x(x + 4) = 3(x + 2) + 6 x2 + 4x = 3x + 6 + 6 x2 + 4x = 3x + 12 -12 -3x -3x -12 x2 + x – 12 = 0 (x + 4)(x – 3) = 0x + 4 = 0 x – 3 = 0 -4 -4 +3 +3 x = -4 x = 3

Answer: 7

Let x = 1st COI x + 2 = 2nd COI x + 4 = 3rd COI

6. The length and width of a rectangle are in the ratio 2:3. The area of the rectangle is 150 square feet

Let length = 2x width = 3x2(5) = 103(5) = 15

A = lw 150 = 2x (3x) 150 = 6x2 -150 -150 0 = 6x2 – 150 0 = 6(x2 – 25) 0 = 6(x + 5)(x – 5) 0 = x + 5 x – 5 = 0-5 -5 +5 +5-5 = x x = 5

Answer: The length is 10 feet and the width is 15 feet.

7. The length of a rectangle is 7 meters more than twice the width.  Find the dimensions if the area is 60 square meters.

Let length = 2x + 7 width = x

2(4) + 7 = 15

A = lw 60 = x(2x + 7) 60 = 2x2 + 7x -60 -60 0 = 2x2 + 7x – 60 0 = 2x2 – 8x + 15x – 60 0 = (2x2 – 8x) + (15x – 60) 0 = 2x(x – 4) + 15(x – 4) 0 = (2x + 15)(x – 4) 0 = 2x + 15 x – 4 = 0-15 -15 +4 +4-15 = 2 x x = 4 2 2

Answer: The length is 15 feet and the width is 4 feet.

8. Solve: 12x2 = 27

12x2 = 27 -27 -2712x2 – 27 = 03(x2 – 9) = 03(x + 3)(x – 3) = 00 = x + 3 x – 3 = 0-3 -3 +3 +3-3 = x x = 3

9. Solve: 5x2 – 11x = 12

5x2 – 11x = 12 -12 -125x2 – 11x – 12 = 05x2 – 15x + 4x – 12 = 05x(x – 3) + 4(x – 3) = 0(5x + 4)(x – 3) = 00 = 5x + 4 x – 3 = 0-4 -4 +3 +3-4 = 5x x = 3 5 5 x = -4/5

10. Solve: 6x2 + 46x – 16 = 0

6x2 + 46x – 16 = 0 2(3x2 + 23x – 8) = 0 2(3x2 – x + 24x – 8) = 02 ≠ 0 (3x2 – x) + (24x – 8) = 0x(3x – 1) + 8(3x – 1) = 0(3x – 1)(x + 8) = 00 = 3x – 1 x + 8 = 0+1 +1 -8 -81 = 3x x = -83 3 x = 1/3