The first term is, 4x2 its coefficient is 4 .
The middle term is, -23x its coefficient is -23 .
The last term, "the constant", is -6
Step-1 : Multiply the coefficient of the first term by the constant 4 • -6 = -24
Step-2 : Find two factors of -24 whose sum equals the coefficient of the middle term, which is -23 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -24 and 1
4x2 - 24x + 1x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (x-6)
Add up the last 2 terms, pulling out common factors :
1 • (x-6)
Step-5 : Add up the four terms of step 4 :
(4x+1) • (x-6)
Which is the desired factorization
