What are the factors of 27x^2 − 9x − 6?
To find the factors of the given expression, we can factor it by grouping.
First, let's rearrange the terms of the expression in descending order:
27x^2 - 9x - 6
Next, we look for common factors among the terms. In this case, the common factor is 3:
3(9x^2 - 3x - 2)
Next, we look for a pair of numbers whose product is equal to the constant term (-2) and whose sum is equal to the coefficient of the middle term (-3). In this case, the numbers are -2 and 1:
3(9x^2 - 3x - 2)
= 3(9x^2 - 6x + 3x - 2)
= 3(3x(3x - 2) + 1(3x - 2))
Now, we can factor out the common binomial factor (3x - 2):
3(3x(3x - 2) + 1(3x - 2))
= 3(3x + 1)(3x - 2)
Therefore, the factors of 27x^2 - 9x - 6 are: 3, (3x + 1), and (3x - 2).