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X-box Factoring Quadratics February 5, 2016

X-box Factoring Quadratics February 5, 2016. Factor the x-box way. y = ax 2 + bx + c. x. q. Product a c. First and Last Coefficients. 1st Term. Factor q. x. q. p. Middle. Last term. Factor p. p. b= p + q Sum. Factor the x-box way. Example: Factor 3x 2 -13x -10.

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X-box Factoring Quadratics February 5, 2016

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  1. X-box Factoring QuadraticsFebruary 5, 2016

  2. Factor the x-box way y = ax2 + bx + c x q Product ac First and Last Coefficients 1st Term Factor q x q p Middle Last term Factor p p b= p + q Sum

  3. Factor the x-box way Example: Factor 3x2 -13x -10 (3)(-10)= -30 x -5 3x 3x2 -15x 2 -15 -13 -10 2x +2 3x2 -13x -10 = (x-5)(3x+2)

  4. Factor the x-box way Example: Factor 2x2 + 11x + 5 (2)(5) = 10 5 x 2x 2x2 10x 10 1 11 5 x 1 2x2 + 11x + 5 = (2x + 1)(x +5)

  5. Factor the x-box way Example: Factor 5w2 – 9w -2 (5)(-2) = -10 -2 w 5w 1 5w2 -10x -10 1 -9 -2 w 5w2 – 9w -2 = (5w+1)(w-2)

  6. -12 4 Examples Factor using the x-box method. 1. x2 + 4x – 12 a) b) x +6 x26x -2x -12 x 6 -2 -2 Solution: x2 + 4x – 12 = (x + 6)(x - 2)

  7. Examples continued 2x2 + 19 -10 X 10 -20 20 -1 19 2x x220x -1x 10 -1 Solution: 2x2 + 19 -10 = (2x-1)(x+10)

  8. Think-Pair-Share • Based on the problems we’ve done, list the steps in the diamond/box factoring method so that you could teach someone else can do a problem. 2. Trade papers with your partner and use their steps to factor the following problem: 3b2 + 26b +35

  9. Trying out the Steps • If you cannot complete the problem using only the steps written, put an arrow on the step where you stopped. Give your partner’s paper back to him. • Modify the steps you wrote to correct any incomplete or incorrect steps. Finish the problem based on your new steps and give the steps back to your partner. • Try using the steps again to factor: 3x2 - 17x -6.

  10. Examples 2x2 - 5x - 7 2x -7 x 2x2-7x 2x -7 +1 Solution: 2x2 - 5x – 7 = (2x - 7)(x + 1)

  11. Examples 15x2 + 7x - 2 a) b) 3x +2 -30 7 5x 15x210x -3x -2 10-3 -1 Solution: 15x2 + 7x – 2 = (3x + 2)(5x - 1)

  12. Independent Practice Show all work.

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