Solution - Simplification or other simple results

Step  1  :

Step  2  :

Pulling out like terms :

 2.1     Pull out like factors :

   -x² + 70x - 600  =   -1 • (x² - 70x + 600) 

Trying to factor by splitting the middle term

 2.2     Factoring  x² - 70x + 600 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -70x  its coefficient is  -70 .
The last term, "the constant", is  +600 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 600 = 600 

Step-2 : Find two factors of  600  whose sum equals the coefficient of the middle term, which is   -70 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -60  and  -10 
                     x² - 60x - 10x - 600

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-60)
              Add up the last 2 terms, pulling out common factors :
                    10 • (x-60)
Step-5 : Add up the four terms of step 4 :
                    (x-10)  •  (x-60)
             Which is the desired factorization

Final result :

  (10 - x) • (x - 60)