Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((44•(k5))-(66•(k4)))+(7•11k3)
 Step  2  :

Equation at the end of step  2  :

  ((44 • (k5)) -  (2•3•11k4)) +  (7•11k3)
 Step  3  :

Equation at the end of step  3  :

  ((22•11k5) -  (2•3•11k4)) +  (7•11k3)

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   44k⁵ - 66k⁴ + 77k³  =   11k³ • (4k² - 6k + 7) 

Trying to factor by splitting the middle term

 5.2     Factoring  4k² - 6k + 7 

The first term is,  4k²  its coefficient is  4 .
The middle term is,  -6k  its coefficient is  -6 .
The last term, "the constant", is  +7 

Step-1 : Multiply the coefficient of the first term by the constant   4 • 7 = 28 

Step-2 : Find two factors of  28  whose sum equals the coefficient of the middle term, which is   -6 .

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :

  11k3 • (4k2 - 6k + 7)