X^3-4x^2+5x+1/x^2+x-1

(x3-4x2+5x+1)/x2+x-1  

Final result :

 2x3 - 5x2 + 5x + 1

 ——————————————————

         x2        

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

  x3)-22x2)+5x)+1)

 (————————————————————+x)-1

           x2          

Step  2  :

           x3 - 4x2 + 5x + 1

Simplify   —————————————————

                  x2        

Checking for a perfect cube :

2.1    x3 - 4x2 + 5x + 1  is not a perfect cube  

Trying to factor by pulling out :

2.2      Factoring:  x3 - 4x2 + 5x + 1  

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

Group 1:  5x + 1  

Group 2:  x3 - 4x2  

Pull out from each group separately :

Group 1:   (5x + 1) • (1)

Group 2:   (x - 4) • (x2)

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.

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step-by-step explanation: