What is the factored form of the expression? 12d2 + 4d – 1
a. (6d + 1)(2d + 1)
b. (6d – 1)(2d – 1)
c. (6d – 1)(2d + 1)
d. (6d + 1)(2d – 1)

12d^2 + 4d -1   

This is a quadratic expression and we would use factorization method.

Multiply the first and the last terms   12d^2 * -1 = -12d^2

Next, we think of two factors that multiply to give -12d^2 and add up to give the middle term +4d.

So the factors are 6d and -2d,   
Check:    6d*-2d = -12d^2
               6d + (-2d) = 6d -2d = 4d

So we replace the middle term +4d with (6d - 2d)

12d^2 + 4d -1   
12d^2 +6d - 2d -1   
6d(2d + 1) -1(2d +1)       Factorize out (2d+1)

(2d+1)(6d - 1) 
(6d -1)(2d+1).

Option C.