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.