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Factor By Grouping               By L.D.
Problem 1 Factor 5(x + 8) + 3x(x + 8)
Problem 1 Factor 5(x + 8) + 3x(x + 8)The first thing we do to solve this is separate the problem up.Since the things in p...
Problem 1 Factor 5(x + 8) + 3x(x + 8) (x + 8)The second things we must do is look at the problem withoutthe parenthesis ...
Problem 1 Answer (5 + 3x)(x + 8)
Practice Factor 2x (x – 5) + 3 (x -5) x2 (y – 3) – 8 (y – 3)
Practice Factor 2x (x – 5) + 3 (x -5)    (2x + 3)(x – 5) x2 (y – 3) – 8 (y – 3)   (x2 – 8)(y – 3)
Problem 2 Factor y3 – 4y2 + 8y - 32
Problem 2 Factor y3 – 4y2 + 8y – 32The first thing we need to do here is to get this into the properformat. So we need to...
Problem 2 Factor y3 – 4y2 + 8y – 32 y2(y – 4) & 8(y – 4)Now that we have the GCFs, we will combine the problem andmake t...
Problem 2 Factor y3 – 4y2 + 8y – 32 y2(y – 4) & 8(y – 4) y2(y – 4) + 8(y – 4)Now we create our problem by slapping the ...
Problem 2 Answer Factor y3 – 4y2 + 8y – 32 (y2+ 8)(y – 4)
Practice 5w + 10 + 3xw + 6x 2wx + 10w + 7x + 35 a3 + 6a – 5a2 – 30
Practice 5w + 10 + 3xw + 6x    (5 + 3x)(w + 2) 2wx + 10w + 7x + 35 (2w + 7)(x + 5) a3 + 6a – 5a2 – 30    (a – 5)(a + 6)...
Bonus x(13 + x) – (x + 13)
Bonus x(13 + x) – (x + 13)In this problem we will fill up the emptiness next to the dividingline by make visible the ever...
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Factor by grouping

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Factor by grouping

  1. 1. Factor By Grouping By L.D.
  2. 2. Problem 1 Factor 5(x + 8) + 3x(x + 8)
  3. 3. Problem 1 Factor 5(x + 8) + 3x(x + 8)The first thing we do to solve this is separate the problem up.Since the things in parenthesis on both sides are the same, wewill smash them together and combine them to make a single (x+ 8). I will turn them red on the next slide to show we mustn’ttouch them now.
  4. 4. Problem 1 Factor 5(x + 8) + 3x(x + 8) (x + 8)The second things we must do is look at the problem withoutthe parenthesis problems. What we see is 5 + 3x, so we will placethat in parenthesis and let is sit next to our combined (x + 8) tomake our answer which is on the next slide.
  5. 5. Problem 1 Answer (5 + 3x)(x + 8)
  6. 6. Practice Factor 2x (x – 5) + 3 (x -5) x2 (y – 3) – 8 (y – 3)
  7. 7. Practice Factor 2x (x – 5) + 3 (x -5) (2x + 3)(x – 5) x2 (y – 3) – 8 (y – 3) (x2 – 8)(y – 3)
  8. 8. Problem 2 Factor y3 – 4y2 + 8y - 32
  9. 9. Problem 2 Factor y3 – 4y2 + 8y – 32The first thing we need to do here is to get this into the properformat. So we need to split the problem in half using the + as adividing line, like a wall and then we need to find the GCF of theproblems on separate sides of the wall.
  10. 10. Problem 2 Factor y3 – 4y2 + 8y – 32 y2(y – 4) & 8(y – 4)Now that we have the GCFs, we will combine the problem andmake the 8 have a plus in front of it as it is positive.y2(y – 4) + 8(y – 4)
  11. 11. Problem 2 Factor y3 – 4y2 + 8y – 32 y2(y – 4) & 8(y – 4) y2(y – 4) + 8(y – 4)Now we create our problem by slapping the parenthesistogether and adding the y2 and 8.
  12. 12. Problem 2 Answer Factor y3 – 4y2 + 8y – 32 (y2+ 8)(y – 4)
  13. 13. Practice 5w + 10 + 3xw + 6x 2wx + 10w + 7x + 35 a3 + 6a – 5a2 – 30
  14. 14. Practice 5w + 10 + 3xw + 6x (5 + 3x)(w + 2) 2wx + 10w + 7x + 35 (2w + 7)(x + 5) a3 + 6a – 5a2 – 30 (a – 5)(a + 6)The reason the last one is came out like this is becaus, when Ilooked at the second half with the negative dividing line, Idecided to take -5 out of the -5a2.a3 + 6a – 5a2 – 30a(a2 + 6) – 5(a2 – 6)(a – 5)(a2 + 6)
  15. 15. Bonus x(13 + x) – (x + 13)
  16. 16. Bonus x(13 + x) – (x + 13)In this problem we will fill up the emptiness next to the dividingline by make visible the ever invisible 1. We can then solve theproblem as we always have. We will then get (x - 1)(13 + x)

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