Solve: 12 = x2 - 6x - 4

 2 • (6x2 - 3x - 2)

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((22•3x2) -  6x) -  4

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  12x2 - 6x - 4  =   2 • (6x2 - 3x - 2)

Trying to factor by splitting the middle term

3.2     Factoring  6x2 - 3x - 2

The first term is,  6x2  its coefficient is  6 .

The middle term is,  -3x  its coefficient is  -3 .

The last term, "the constant", is  -2

Step-1 : Multiply the coefficient of the first term by the constant   6 • -2 = -12

Step-2 : Find two factors of  -12  whose sum equals the coefficient of the middle term, which is   -3 .

     -12    +    1    =    -11

     -6    +    2    =    -4

     -4    +    3    =    -1

     -3    +    4    =    1

     -2    +    6    =    4

     -1    +    12    =    11

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

 2 • (6x2 - 3x - 2)

Hope this helped!

-Rin

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