Box Method Factoring
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The document provides instructions and examples for factoring quadratic expressions using the box method. It explains the steps as: 1) Draw a box and write the coefficients of the quadratic term, linear term, and constant term. 2) Find two numbers whose sum is the linear coefficient and whose product is the constant term. 3) Write these two numbers above and below the box to factor the expression. Several examples are worked out step-by-step and the reader is prompted to try additional problems and check their own work.
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Box Method Factoring
- 2. Factor the box method way Middle b=m+n Sum Product ac=mn m n First and Last Coefficients y = ax2 + bx + c Last term 1st Term Factor n Factor m Base 1 Base 2 GCF Height
- 3. Examples: Factor using the x-box method. 1. x2 + 4x – 12 a) b) x -12 4 6 -2 x2 6x -2x -12 x -2 +6 Solution: x2 + 4x – 12 = (x + 6)(x - 2)
- 4. You Try: 2. x2 - 9x + 20 a) b) 20 -9
- 5. 2. x2 - 9x + 20 a) b) 20 -9 x2 -4x -5x 20 x x -4 -5 Solution: x2 - 9x + 20 = (x - 4)(x - 5) -4 -5 Check yourself:
- 6. Think-Pair-Share 1. Try this problem using the box method: x2 +4x -32. 2. Trade papers with your partner and use their steps to factor the following problem: x2 +4x -32.
- 7. Examples: 3. 2x2 - 5x - 7 a) b) -14 -5 2x2 -7x 2x -7 x 2x -7 +1 Solution: 2x2 - 5x – 7 = (2x - 7)(x + 1) -7 2
- 8. You Try: 3. 15x2 + 7x - 2 a) b) -30 7
- 9. Check Yourself: 3. 15x2 + 7x - 2 a) b) -30 7 15x2 10x -3x -2 5x 3x +2 -1 Solution: 15x2 + 7x – 2 = (3x + 2)(5x - 1) 10 -3
- 10. Check Yourself: 3. 15x2 + 7x - 2 a) b) -30 7 15x2 10x -3x -2 5x 3x +2 -1 Solution: 15x2 + 7x – 2 = (3x + 2)(5x - 1) 10 -3