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Factor Quadratic Trinomials: The X-Box Method

Learn to factor quadratic trinomials using the X-Box method. Understand when to use the box and X, and practice with examples. Helpful hints and a fun song included!

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Factor Quadratic Trinomials: The X-Box Method

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  1. Warmup Factor. 1. GCF 2. GCF 3. Grouping/GCF 4. Grouping

  2. 4.4 Factoring Trinomials Day 3 a=1 and a>1 Objective: To factor quadratic trinomials.

  3. Remember… (x+2)(x+5) We used double distribution to multiply this. Today, we are going to work BACKWARDS!  New method…. The X!!

  4. Example 1 x2 + 14x + 45 1st•3rd 2nd 45 9 5 14 Pick 2 #s that multiply to get the top and add to get the bottom. Those go on the sides of the X. (x + 9)(x + 5)

  5. When a=1 you don’t have to use the box When a=1 No box is necessary When a>1 you have to use the x and the box

  6. When a>1 you must use the x and the box. • This song will “teach you how to factor” • https://youtu.be/OFSrINhfNsQ

  7. Factor the x-box way y = ax2 + bx + c Base 1 Base 2 Product ac=mn First and Last Coefficients 1st Term Factor n GCF n m Middle Last term Factor m b=m+n Sum Height

  8. 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)

  9. -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)

  10. Examples continued 2. x2 - 9x + 20 a) b) x -4 -4-5 20 -9 x2-4x -5x 20 x -5 Solution: x2 - 9x + 20 =(x - 4)(x - 5)

  11. Think-Pair-Share • Based on the problems we’ve done, list the steps in the diamond/box factoring method so that someone else can do a problem using only your steps. 2. Trade papers with your partner and use their steps to factor the following problem: x2 +4x -32.

  12. Try w/ a partner 

  13. You are up 6y2 – 13y – 5 1st•3rd 2nd -30 -15 2 -13 (2y – 5)(3y + 1)

  14. You can do it continued 3. 2x2 - 5x - 7 a) b) 2x -7 -72 -14 -5 x 2x2-7x 2x -7 +1 Solution: 2x2 - 5x – 7 = (2x - 7)(x + 1)

  15. Keep up the good work 3. 15x2 + 7x - 2 a) b) 3x +2 -30 7 5x 15x210x -3x -2 10-3 -1 Solution: 15x2 + 7x – 2 = (3x + 2)(5x - 1)

  16. TOO

  17. Example 3 So what is another way we can solve this if we can’t factor? How many solutions does this have? How can you tell?

  18. Helpful X hints. + + + + - - + - - - + big - small - big + small + -

  19. Mixed Review PRACTICE! • GCF • Difference of Squares • Perfect Squares • Difference of Cubes • Grouping • Trinomials x2 + 8x + 16

  20. Homework • Factoring WS #3

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