Which of the following is a factor of -12k^2-36k-27?
6k-9
2k+3
-6k+9
2k-3
To find out which of the following is a factor of -12k^2-36k-27, we can use the Remainder Theorem. According to the Remainder Theorem, if a polynomial f(x) is divided by x-a and the remainder is 0, then x-a is a factor of f(x).
Let's check each option:
1. 6k-9: If we divide -12k^2-36k-27 by 6k-9, we get a quotient of -2k-3 and a remainder of 0. Therefore, 6k-9 is a factor of -12k^2-36k-27.
2. 2k+3: If we divide -12k^2-36k-27 by 2k+3, we get a quotient of -6k-9 and a remainder of 0. Therefore, 2k+3 is a factor of -12k^2-36k-27.
3. -6k+9: If we divide -12k^2-36k-27 by -6k+9, we get a quotient of 2k+3 and a remainder of 0. Therefore, -6k+9 is a factor of -12k^2-36k-27.
4. 2k-3: If we divide -12k^2-36k-27 by 2k-3, we get a quotient of -6k-9 and a remainder of 0. Therefore, 2k-3 is a factor of -12k^2-36k-27.
Therefore, all of the given options are factors of -12k^2-36k-27.