QUESTÕES RESOLVIDAS FATORAÇÃO

Simplifique as expressões fatorando o numerador e o denominador:

1)    __x² – 144____  =  (x + 12)(x – 12) = x – 12

         x² + 24x + 144         (x + 12)²               x + 12

2)    __x² +22x + 121 =  (x + 11)²  = x + 11

                   x + 11            x + 11

3)    x² - 100 = ( x – 10)(x + 10) = x + 10

        x – 10              x – 10

4)  x² + 5x = x.( x + 5) = x

      x + 5          x + 5

5) 4x – 8 = 4.(x - 2) = 4

     x – 2        x – 2

6) 5x + 10 = 5.(x + 2)   = 1

   10x + 20   10.(x + 2)     2

7) a² – ab = a.( a – b) = a

     a – b          a – b

8) x² + 3x = x.(x + 3) = x

    4x + 12    4.(x + 3)    4

9)       7c – 21 = 7.(c – 3) =      7

    c² – 6c + 9     (c – 3)²       c - 3

10) x² – 16x + 64   =         (x – 8)²  = x – 8

          x² – 64            (x – 8)(x + 8)     x + 8

11)          m² – 25 = (m – 5)(m + 5) = m - 5

     m² + 10m + 25       (m + 5)²           m + 5

12) 4x² – 4x + 1 =     (2x – 1 )²            = 2x – 1

          4x² – 1         (2x – 1)(2x + 1)        2x + 1

13) x² + 6x + 9 =   (x + 3)²  = x + 3

          x + 3              x + 3

14) a³ – ab²   =  a.(a² – b²) = a.(a – b)(a + b) = a – b

      a.( a + b)      a.(a + b)      a(a + b)

15) a² + ab – ac – bc = a.(a + b) – c.(a + b) = (a + b)(a – c) = a + b

             a² – ac                    a.(a – c)                   a.(a – c)             a

16) 9x² – 6x + 1 =       (3x – 1)²          =   3x – 1

          9x² – 1          (3x – 1)(3x + 1)         3x + 1

17) x² + 5x + ax + 5a = x.(x + 5) + a.( x + 5) = (x + 5)(x + a) = x + a

            2x + 10                          2.(x + 5)              2.( x + 5)           2

18) 7a – 7b + am – bm = 7(a – b) + m(a – b)  = (a – b)(7 + m)  =  7 + m

           a² – 2ab + b²                  (a – b)²                         (a – b)²              a – b

19) x³ – x² + 6x – 6 =  x².(x – 1) + 6.(x – 1)  = (x – 1)(x² + 6)  =     x² + 6

     7x⁵ – 14x⁴ + 7x³       7x³.(x² – 2x + 1)              7x³. (x – 1)²      7x³ .(x – 1)

20)             4a² – 9b² =  (2a – 3b)(2a + 3b)  = 2a – 3b

      4a² + 12ab + 9b²           (2a + 3b)²              2a + 3b

21) x² + 4x + 3 =  (x + 1)(x + 3)  =  x  + 1

      x² + 6x + 9         (x + 3)²            x + 3

22) x² – 6x + 8 = ( x – 2)(x – 4) =  x – 4

         x² – 4          (x – 2)(x + 2)      x + 2

23) x² + x – 6 = (x – 2)(x + 3)  =  x + 3

      x² – 4x + 4      (x – 2)²             x – 2

24) x² – 5x + 4 = (x – 1)(x – 4) =  x – 4

       x² – 2x + 1        (x – 1)²           x - 1

25) 3x² – 18x + 27 = 3.(x² – 6x + 9)  = 3.(x – 3)²  = x - 3

          3x² – 9x              3x. (x – 3)        3x.(x – 3)       x

26) 4x² + 20x + 25 =       (2x + 5)²         =  2x + 5

           4x² – 25           (2x – 5)(2x + 5)       2x – 5  

27) xy² – 2xy =  xy.(y – 2)      =       xy

        y² – 4         (y – 2)(y +2)       y +2

28) x² – 4x + 4 =  (x – 2)²      =   x – 2

         xy – 2y        y.(x – 2)            y

29) a² – 2ab + b² =  (a – b)²   =   a – b

           2a – 2b         2.(a – b)         2

30)      a² – b²       =  (a – b)(a + b)  = a – b

      a² + 2ab + b²         (a + b)²              a + b