Solution - Simplification or other simple results

Step  1  :

Step  2  :

Pulling out like terms :

 2.1     Pull out like factors :

   -x² + 8x - 7  =   -1 • (x² - 8x + 7) 

Trying to factor by splitting the middle term

 2.2     Factoring  x² - 8x + 7 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -8x  its coefficient is  -8 .
The last term, "the constant", is  +7 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 7 = 7 

Step-2 : Find two factors of  7  whose sum equals the coefficient of the middle term, which is   -8 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  -1 
                     x² - 7x - 1x - 7

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-7)
              Add up the last 2 terms, pulling out common factors :
                     1 • (x-7)
Step-5 : Add up the four terms of step 4 :
                    (x-1)  •  (x-7)
             Which is the desired factorization

Final result :

  (1 - x) • (x - 7)