Factor completely. \[ 9 x^{4}+21 x^{3}-9 x^{2}-21 x \] Select one: a. $-3 x(3 x+7)(x+1)(x-1)$ b. $3 x(3 x-7)(x+1)(x-1)$ c. $3 x(3 x+7)(x+1)(x-1)$ d. $3 x(3 x+7)(x+1)^{2}$

Step 1 ：Given the polynomial \(9x^{4} + 21x^{3} - 9x^{2} - 21x\), we are asked to factor it completely.

Step 2 ：Factoring out the common factor of 3x, we get \(3x(3x^{3} + 7x^{2} - 3x - 7)\).

Step 3 ：Next, we factor the cubic polynomial inside the parentheses. We can do this by grouping the terms and factoring out common factors. This gives us \(3x((x - 1)(3x^{2} + 7x + 3))\).

Step 4 ：Finally, we factor the quadratic polynomial inside the parentheses. This gives us \(3x(x - 1)(x + 1)(3x + 7)\).

Step 5 ：Comparing this with the given options, we see that it matches with option c.

Step 6 ：So, the correct answer is option c.