Question

factors of the polynomial xsquare-23x+108

Answer 1

x2-3x-108 

Final result :

(x + 9) • (x - 12)

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  x2-3x-108 

The first term is,  x2  its coefficient is  1 .
The middle term is,  -3x  its coefficient is  -3 .
The last term, "the constant", is  -108 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -108 = -108 

Step-2 : Find two factors of  -108  whose sum equals the coefficient of the middle term, which is   -3 .
     -108   +   1   =   -107     -54   +   2   =   -52     -36   +   3   =   -33     -27   +   4   =   -23     -18   +   6   =   -12     -12   +   9   =   -3   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -12  and  9 
                     x2 - 12x + 9x - 108

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-12)
              Add up the last 2 terms, pulling out common factors :
                    9 • (x-12)
Step-5 : Add up the four terms of step 4 :
                    (x+9)  •  (x-12)
             Which is the desired factorization

Final result :

(x + 9) • (x - 12)