x = -1
 x =(1-√5)/-2= 0.618
 x =(1+√5)/-2=-1.618
Step  1  :
Equation at the end of step  1  :
  0 -  (((x3) +  2x2) -  1)  = 0  
Step  2  :  
Step  3  :
Pulling out like terms :
 3.1     Pull out like factors :
   -x3 - 2x2 + 1  =   -1 • (x3 + 2x2 - 1)  
 3.2    Find roots (zeroes) of :       F(x) = x3 + 2x2 - 1
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient
In this case, the Leading Coefficient is  1  and the Trailing Constant is  -1.
 The factor(s) are:
of the Leading Coefficient :  1
 of the Trailing Constant :  1
 Let us test ....
  	P    Q    P/Q    F(P/Q)    	Divisor
      -1       1        -1.00        0.00      x + 1  
      1       1        1.00        2.00      
The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms
In our case this means that
   x3 + 2x2 - 1  
can be divided with  x + 1  
Polynomial Long Division :
 3.3    Polynomial Long Division
Dividing :  x3 + 2x2 - 1  
                              ("Dividend")
By         :    x + 1    ("Divisor")
dividend     x3  +  2x2      -  1  
- divisor  * x2     x3  +  x2          
remainder         x2      -  1  
- divisor  * x1         x2  +  x      
remainder          -  x  -  1  
- divisor  * -x0          -  x  -  1  
remainder                0
Quotient :  x2+x-1  Remainder:  0  
Trying to factor by splitting the middle term
 3.4     Factoring  x2+x-1  
The first term is,  x2  its coefficient is  1 .
The middle term is,  +x  its coefficient is  1 .
The last term, "the constant", is  -1  
Step-1 : Multiply the coefficient of the first term by the constant   1 • -1 = -1  
Step-2 : Find two factors of  -1  whose sum equals the coefficient of the middle term, which is   1 .
      -1    +    1    =    0  
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step  3  :
  (-x2 - x + 1) • (x + 1)  = 0  
Step  4  :
Theory - Roots of a product :
 4.1    A product of several terms equals zero.  
 When a product of two or more terms equals zero, then at least one of the terms must be zero.  
 We shall now solve each term = 0 separately  
 In other words, we are going to solve as many equations as there are terms in the product  
 Any solution of term = 0 solves product = 0 as well.
Parabola, Finding the Vertex :
 4.2      Find the Vertex of   y = -x2-x+1
 For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -0.5000  
 Plugging into the parabola formula  -0.5000  for  x  we can calculate the  y -coordinate :  
  y = -1.0 * -0.50 * -0.50 - 1.0 * -0.50 + 1.0
or   y = 1.250
Parabola, Graphing Vertex and X-Intercepts :
Root plot for :  y = -x2-x+1
Axis of Symmetry (dashed)  {x}={-0.50}  
Vertex at  {x,y} = {-0.50, 1.25}  
 x -Intercepts (Roots) :
Root 1 at  {x,y} = { 0.62, 0.00}  
Root 2 at  {x,y} = {-1.62, 0.00}  
Solve Quadratic Equation by Completing The Square
 4.3     Solving   -x2-x+1 = 0 by Completing The Square .
 Multiply both sides of the equation by  (-1)  to obtain positive coefficient for the first term:
 x2+x-1 = 0  Add  1  to both side of the equation :
   x2+x = 1
Now the clever bit: Take the coefficient of  x , which is  1 , divide by two, giving  1/2 , and finally square it giving  1/4  
Add  1/4  to both sides of the equation :
  On the right hand side we have :
   1  +  1/4    or,  (1/1)+(1/4)  
  The common denominator of the two fractions is  4   Adding  (4/4)+(1/4)  gives  5/4  
  So adding to both sides we finally get :
   x2+x+(1/4) = 5/4
Adding  1/4  has completed the left hand side into a perfect square :
   x2+x+(1/4)  =
   (x+(1/2)) • (x+(1/2))  =
  (x+(1/2))2
Things which are equal to the same thing are also equal to one another. Since
   x2+x+(1/4) = 5/4 and
   x2+x+(1/4) = (x+(1/2))2
then, according to the law of transitivity,
   (x+(1/2))2 = 5/4
We'll refer to this Equation as  Eq. #4.3.1  
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
   (x+(1/2))2   is
   (x+(1/2))2/2 =
  (x+(1/2))1 =
   x+(1/2)
Now, applying the Square Root Principle to  Eq. #4.3.1  we get:
   x+(1/2) = √ 5/4
Subtract  1/2  from both sides to obtain:
   x = -1/2 + √ 5/4
Since a square root has two values, one positive and the other negative
   x2 + x - 1 = 0
   has two solutions:
  x = -1/2 + √ 5/4
   or
  x = -1/2 - √ 5/4
Note that  √ 5/4 can be written as
  √ 5  / √ 4   which is √ 5  / 2
Solve Quadratic Equation using the Quadratic Formula
 4.4     Solving    -x2-x+1 = 0 by the Quadratic Formula .
 According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :
                                      
            - B  ±  √ B2-4AC
  x =   ————————
                      2A
  In our case,  A   =     -1
                      B   =    -1
                      C   =   1
Accordingly,  B2  -  4AC   =
                     1 - (-4) =
                     5
Applying the quadratic formula :
               1 ± √ 5
   x  =    ————
                   -2
  √ 5   , rounded to 4 decimal digits, is   2.2361
 So now we are looking at:
           x  =  ( 1 ±  2.236 ) / -2
Two real solutions:
 x =(1+√5)/-2=-1.618
or:
 x =(1-√5)/-2= 0.618
Solving a Single Variable Equation :
 4.5      Solve  :    x+1 = 0  
 Subtract  1  from both sides of the equation :  
                      x = -1
Hope this helps.