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)