((12 * (x
The first term is, 3x
The middle term is, -13x its coefficient is -13.
The last term, "the constant", is -10
Step-1 : Multiply the coefficient of the first term by the constant 3 * -10 = -30
Step-2 : Find two factors of -30 whose sum equals the coefficient of the middle term, which is -13.
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 2.
Step-4 : Add up the first 2 terms, pulling out like factors :
3x * (x-5)
Add up the last 2 terms, pulling out common factors:
2 * (x-5)
Step-5 : Add up the four terms of step 4:
(3x+2) * (x-5)
Which is the desired factorization
Answer: 4x * (x-5) * (3x+2)