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By The Number One Dummy: Juan Jimenez

factoring for dummies

Difference of cubes

Rule : (a^2 - b^2)

(a + b) (a - b)

            You need the negative for the equation to result the same as the first.

Example #1:

9x^2 - 49x^2

now separate it…factor it.

(3x - 7)(3x + 7)

Example #2: 

72a^4 - 2

 GFC

2(36a^4 - 1)

 factor                                                                                                                                    

2(6a^2 + 1)(6a^2 - 1)

Example #3:

10c^5 - 10c

 GFC

10c(1w^4 - 1)

Factor

10c(1w^2 + 1)(1w^2 - 1)



Sum of cubes (easy)

Rule: (a^3 + b^3)

(a+b)(a^2 - ab + b)

this is just a and  b before being cubed.


Example #1:

x^3 + 273

x^3 is a^3 and 27 is b^3


Now put them how they looked before being cubed.


(x)^3 + (3)^3

 now plug them in

((x) + (3))((x)^2 - (3)(x) + (3)^2)

 which looks like

(x + 3)(x^2 - 3x + 9)


Example#2:

n^3 + 216m^3

(n)^3 + (6m)^3

(n+6m)(n^2 - 6mn + 36m^2)


Example#3:

500a^3 + 4

4(125a^3 + 1)

(5a)^3 + (1)^3

(5a+1)(25a^2 - 5a + 1)


Difference Of Cubes.

(this just means that instead of plus you use minus)

Rule: a^3 - b^3

    only difference is the negative

(a - b)(a^2 + ab + b2)

           these are the important parts 

Example#1:

x^3 - 1

(x)^3 - (1)^3

(x - 1)(x^2 + 1x + 1)

Example#2:

4 - 32h^3

4(1 - 8h^3)

(1)^3 - (2h)^3

4(1 - 2h)(1 + 2h + 4h^2)

Example#3:

216k^3 - 125

(6k)^3 - (5)^3

(6k - 5)(36k - 30k + 25)

Four terms

Rule : USE GROUPING !!!!!!!

STEPS:

  1. Group first and last 2 terms

  2. Factor GCF

  3. Factor common binomial

Example#1:

4x^3 - 5x^2 - 16x+20

Group

4x^3 - 5x^2             -16x + 20

 Factor

-x^2(-4x + 5)       4(-4x + 5)



Example#2:

x^3 - x^2 + 9x-9

x^3 - x^2              9x-9

x^2(x-1)                9(x-1)

(x2+9) , (x-1)


Example#3:

k^3 + 5k^2 - k-5

k^3 + 5k^2              -k-5            

k^2(k+5)                -k(k+5)



always do GCF

Trinomials (hard but easy)

  1. First we do GCF (greatest common factor)

  2. Then we factor.


Example#1:

2a^3 + 38a^2 + 68a

 GCF

2a(a^2 + 19a + 34)

 Factored

(a + 2)(a + 12)

Example#2:

x^4 + 2n^2 - 24

(n^2 - 4)(n^2 + 6)

Example#3:

x^5 - 24x^3 - 25x

x(x^4 - 24x^2 - 25)

(x^2 - 25)(x^2 + 1)