Question

a3+2a2+2a+1 Divided by a2 +a+1

Answer 1

. In step #03.03 
Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "a2"   was replaced by   "a^2".  1 more similar replacement(s).

Step by step solution :Step  1  :Equation at the end of step  1  : Step  2  : a3 - 2a2 + 2a Simplify ————————————— a - 1 Step  3  :Pulling out like terms :

 3.1     Pull out like factors :

   a3 - 2a2 + 2a  =   a • (a2 - 2a + 2) 

Trying to factor by splitting the middle term

 3.2     Factoring  a2 - 2a + 2 

The first term is,  a2  its coefficient is  1 .
The middle term is,  -2a  its coefficient is  -2 .
The last term, "the constant", is  +2 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 2 = 2 

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

     -2   +   -1   =   -3     -1   +   -2   =   -3     1   +   2   =   3     2   +   1   =   3

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

Polynomial Long Division :

 3.3    Polynomial Long Division 
Dividing :  a2-2a+2 
                              ("Dividend")
By         :    a-1    ("Divisor")

dividend  a2 - 2a + 2 - divisor * a1   a2 - a   remainder  - a + 2 - divisor * -a0   - a + 1 remainder      1 

Quotient :  a-1  
Remainder :  1  

Final result : a • (a2 - 2a + 2) ————————————————— a - 1