Question

Please help me . factor. X^2-29x+100

Answer 1

Step-1 : Multiply the coefficient of the first term by the constant   1 • 100 = 100 

Step-2 : Find two factors of  100  whose sum equals the coefficient of the middle term, which is   -29 .

     -100   +   -1   =   -101     -50   +   -2   =   -52     -25   +   -4   =   -29   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -25  and  -4 
                     x2 - 25x - 4x - 100

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-25)
              Add up the last 2 terms, pulling out common factors :
                    4 • (x-25)
Step-5 : Add up the four terms of step 4 :
                    (x-4)  •  (x-25)
             Which is the desired factorization

Final result : (x - 4) • (x - 25)