What is the quotient (6x^4+15x^3+10x^2+10x+4)/(3x^2+2)

(2x + 1) • (x + 2)

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 (((15 • (x3)) -  (2•5x2)) +  6x) -  4

Step  2  :

Equation at the end of step  2  :

 (((3•5x3) -  (2•5x2)) +  6x) -  4

Step  3  :

Checking for a perfect cube :

3.1    15x3-10x2+6x-4  is not a perfect cube  

Trying to factor by pulling out :

3.2      Factoring:  15x3-10x2+6x-4  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  6x-4  

Group 2:  15x3-10x2  

Pull out from each group separately :

Group 1:   (3x-2) • (2)

Group 2:   (3x-2) • (5x2)

Add up the two groups :

              (3x-2)  •  (5x2+2)  

Which is the desired factorization