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# Diamond and box factoring student version

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DIAMOND & BOX FACTORING

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### Diamond and box factoring student version

1. 1. X-box Factoring
2. 2. X- Box 3 -9 Product Sum
3. 3. Factor the x-box way Middle b= m + n Sum Product a c = m n m n First and Last Coefficients y = ax 2 + bx + c Last term 1st Term Factor n Factor m Base 1 Base 2 GCF Height
4. 4. Examples <ul><li>Factor using the x-box method. </li></ul><ul><li>1. x 2 + 4x – 12 </li></ul><ul><li>a) b) </li></ul>x 6 -2 x 2 6 x -2 x -12 x -2 +6 Solution: x 2 + 4x – 12 = (x + 6 )(x - 2 ) -12 4
5. 5. Examples continued <ul><li>2. x 2 - 9x + 20 </li></ul><ul><li>a) b) </li></ul>20 -9 x 2 -4 x -5 x 20 x x -4 -5 Solution: x 2 - 9x + 20 = (x - 4 )(x - 5 ) -4 -5
6. 6. Examples continued <ul><li>3. 2x 2 - 5x - 7 </li></ul><ul><li>a) b) </li></ul>-14 -5 2x 2 -7 x 2 x -7 x 2x -7 +1 Solution: 2x 2 - 5x – 7 = (2x - 7 )(x + 1 ) -7 2
7. 7. Examples continued <ul><li>3. 15x 2 + 7x - 2 </li></ul><ul><li>a) b) </li></ul>-30 7 15x 2 10 x -3 x -2 5x 3x +2 -1 Solution: 15x 2 + 7x – 2 = (3x + 2 )(5x - 1 ) 10 -3
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