(4x^2+11x+9) / (x+2)

quotient and remander

Two solutions were found :
1 x =(11-√265)/8=-0.660
2 x =(11+√265)/8= 3.410

Step by step solution :
Step  1  :
Equation at the end of step  1  :
  (22x2 -  11x) -  9  = 0
Step  2  :
Trying to factor by splitting the middle term
 2.1     Factoring  4x2-11x-9 

The first term is,  4x2  its coefficient is  4 .
The middle term is,  -11x  its coefficient is  -11 .
The last term, "the constant", is  -9 

Step-1 : Multiply the coefficient of the first term by the constant   4 • -9 = -36 

Step-2 : Find two factors of  -36  whose sum equals the coefficient of the middle term, which is   -11 .
     
-36
   +   
1
   =   
-35

     
-18
   +   
2
   =   
-16

     
-12
   +   
3
   =   
-9

     
-9
   +   
4
   =   
-5

     
-6
   +   
6
   =   
0

     
-4
   +   
9
   =   
5

     
-3
   +   
12
   =   
9

     
-2
   +   
18
   =   
16

     
-1
   +   
36
   =   
35

Iagree that is the answer to the question