Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((6•(v5))-(22•(v4)))+(22•5v3)
 Step  2  :

Equation at the end of step  2  :

  ((6 • (v5)) -  (2•11v4)) +  (22•5v3)
 Step  3  :

Equation at the end of step  3  :

  ((2•3v5) -  (2•11v4)) +  (22•5v3)

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   6v⁵ - 22v⁴ + 20v³  =   2v³ • (3v² - 11v + 10) 

Trying to factor by splitting the middle term

 5.2     Factoring  3v² - 11v + 10 

The first term is,  3v²  its coefficient is  3 .
The middle term is,  -11v  its coefficient is  -11 .
The last term, "the constant", is  +10 

Step-1 : Multiply the coefficient of the first term by the constant   3 • 10 = 30 

Step-2 : Find two factors of  30  whose sum equals the coefficient of the middle term, which is   -11 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  -5 
                     3v² - 6v - 5v - 10

Step-4 : Add up the first 2 terms, pulling out like factors :
                    3v • (v-2)
              Add up the last 2 terms, pulling out common factors :
                    5 • (v-2)
Step-5 : Add up the four terms of step 4 :
                    (3v-5)  •  (v-2)
             Which is the desired factorization

Final result :

  2v3 • (v - 2) • (3v - 5)