Which of the following is a factor of -12k^2-36k-27?
6k-9
2k+3
-6k+9
2k-3
To determine if a binomial is a factor of a given polynomial, we can use long division or synthetic division. Let's use long division.
2k - 3 |-12k^2 - 36k - 27
| -12k^2 + 18k
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-54k - 27
We see that -54k - 27 is not divisible by 2k - 3. Therefore, 2k - 3 is not a factor of -12k^2 - 36k - 27.
Let's try the next option.
2k + 3 |-12k^2 - 36k - 27
| -12k^2 - 18k
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-54k - 27
We see that -54k - 27 is divisible by 2k + 3. Therefore, 2k + 3 is a factor of -12k^2 - 36k - 27.
So, the correct answer is 2k + 3.