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4.4 “Solve ax 2 + bx + c by Factoring”

4.4 “Solve ax 2 + bx + c by Factoring”. Part 1: a 5x 2 – 17x + 6 3x 2 + 20x – 7 . 7x 2 – 20x – 3 4. 3x 2 +5x – 12 . Part 2: Special Patterns - Binomials. Examples: 1. 9x 2 – 64 2. 4x 2 – 81. 16r 2 – 36y 2 81x 2 – 49y 2. Special Patterns Continued: . 4x 2 + 20x + 25

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4.4 “Solve ax 2 + bx + c by Factoring”

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  1. 4.4 “Solve ax2 + bx + c by Factoring” Part 1: a • 5x2 – 17x + 6 • 3x2 + 20x – 7 • 7x2 – 20x – 3 4. 3x2 +5x – 12

  2. Part 2: Special Patterns - Binomials Examples: 1. 9x2 – 64 2. 4x2 – 81 • 16r2– 36y2 • 81x2– 49y2

  3. Special Patterns Continued: • 4x2 + 20x + 25 6. 36m2 – 12m + 1 • 25y2 – 80y + 64 • 4x2 – 28x +49

  4. Part 3: Factor Out Something Common Always check to see if you can do this BEFORE you factor!! Examples: • 5x2 – 45 • -5z2 – 20z • 6x2 – 14x + 8 • 12y2 – 21y + 3 5. –16m2 + 12m

  5. Try These:  1. 3x2– 10x + 8 • 6m2 + m – 15 • 49k2 + 112k + 64 4. 81y2 – 25 • x2 – 225 • –25p2+ 60p – 35

  6. Part 4: Solving the Equations These problems will have an equal sign and may say…Find zeros, roots, solutions…it means the same thing, where the quadratic hits the x-axis. Examples: 1. 3x2 + 10x – 8 = 0 • 5x2– 16x + 15 = 4x – 5 • 4x2 – 17x – 15 = 0 4. 3y2 + 22y + 60 = –14y – 48

  7. Part 5: Word Problems 1. You have made a rectangular quilt measuring 5 feet by 4 feet. You want to use the remaining 10 ft2 of fabric to add a border of uniform width. What is the width of the border?

  8. Another Word Problem 2. You are designing a garden for the grounds of your high school. It will be surrounded by a uniform border of polished stones. The flower bed will be 22 feet by 15 feet and your budget will allow you to cover 120 ft2 of stones. What is the width of the border?

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