Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((23•5p2) -  170p) -  45

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   40p² - 170p - 45  =   5 • (8p² - 34p - 9) 

Trying to factor by splitting the middle term

 3.2     Factoring  8p² - 34p - 9 

The first term is,  8p²  its coefficient is  8 .
The middle term is,  -34p  its coefficient is  -34 .
The last term, "the constant", is  -9 

Step-1 : Multiply the coefficient of the first term by the constant   8 • -9 = -72 

Step-2 : Find two factors of  -72  whose sum equals the coefficient of the middle term, which is   -34 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -36  and  2 
                     8p² - 36p + 2p - 9

Step-4 : Add up the first 2 terms, pulling out like factors :
                    4p • (2p-9)
              Add up the last 2 terms, pulling out common factors :
                     1 • (2p-9)
Step-5 : Add up the four terms of step 4 :
                    (4p+1)  •  (2p-9)
             Which is the desired factorization

Final result :

  5 • (2p - 9) • (4p + 1)