Answer:

 2x • (x - 4)2

Step-by-step explanation:

Step by Step Solution

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Reformatting the input :

CHANGES made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

 (((2•(x3))-(22•3x2))+16x)  

 —————————————————————————•(x-4)

           (x-2)          

STEP  

2

:

Equation at the end of step

2

:

 ((2x3 - (22•3x2)) + 16x)  

 ———————————————————————— • (x - 4)

         (x - 2)          

STEP

3

:

           2x3 - 12x2 + 16x

Simplify   ————————————————

                x - 2      

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  2x3 - 12x2 + 16x  =   2x • (x2 - 6x + 8)  

Trying to factor by splitting the middle term

4.2     Factoring  x2 - 6x + 8  

The FIRST term is,  x2  its coefficient is  1 .

The middle term is,  -6x  its coefficient is  -6 .

The last term, "the constant", is  +8  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 8 = 8  

Step-2 : Find two factors of  8  whose sum equals the coefficient of the middle term, which is   -6 .

     -8    +    -1    =    -9  

     -4    +    -2    =    -6    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  -2  

                    x2 - 4x - 2x - 8

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

                   x • (x-4)

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

                   2 • (x-4)

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

                   (x-2)  •  (x-4)

            Which is the desired factorization

Canceling Out :

4.3    Cancel out  (x-2)  which appears on both sides of the fraction line.

Equation at the end of step

4

:

 2x • (x - 4) • (x - 4)

STEP

5

:

Multiplying EXPONENTIAL Expressions:

5.1    Multiply  (x-4)  by  (x-4)  

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our CASE, the common base is  (x-4)  and the exponents are :

         1 , as  (x-4)  is the same number as  (x-4)1  

and   1 , as  (x-4)  is the same number as  (x-4)1  

The product is therefore,  (x-4)(1+1) = (x-4)2  

Final result :

 2x • (x - 4)2

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