What factors of 12n2- 10n+2

2(2n-1)(3n-1)

Step-by-step explanation:

((22•3n2) -  10n) +  2

STEP  1 :

Equation at the end of step 1

 ((22•3n2) -  10n) +  2

STEP  2 :

STEP  3  :

Pulling out like terms

3.1     Pull out like factors :

  12n2 - 10n + 2  =   2 • (6n2 - 5n + 1)  

Trying to factor by splitting the middle term

3.2     Factoring  6n2 - 5n + 1  

The first term is,  6n2  its coefficient is  6 .

The middle term is,  -5n  its coefficient is  -5 .

The last term, "the constant", is  +1  

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

Step-2 : Find two factors of  6  whose sum equals the coefficient of the middle term, which is   -5 .

     -6    +    -1    =    -7  

     -3    +    -2    =    -5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  -2  

                    6n2 - 3n - 2n - 1

Step-4 : Add up the first 2 terms, pulling out like factors :

                   3n • (2n-1)

             Add up the last 2 terms, pulling out common factors :

                    1 • (2n-1)

Step-5 : Add up the four terms of step 4 :

                   (3n-1)  •  (2n-1)

            Which is the desired factorization

Final result :

 2 • (2n - 1) • (3n - 1)

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