What is the factor of 6x minus 27?

Answer 1

In the case of a binomial in general, the only way you can factor it is by looking for common factors in each term. In other words, check whether there is a common factor (in this case) in "6x" and in "27". If there is, take this factor out.

Answer 2

x6 - 9 = (x3)2 - (3)2

And expansion for a2 - b2 is (a - b)(a + b)

Here a = x3 and b = 3

So, (x3)2 - (3)2 = (x3 - 3)(x3 + 3) = [x3 - (31/3)3][x3 + (31/3)3]

And the expansion for a3 - b3 is (a - b)(a2 + ab + b2)

And the expansion for a3 + b3 is (a + b)(a2 - ab + b2)

Here a =x and b = 31/3

So, [x3 - (31/3)3][x3 + (31/3)3] = {(x - 31/3)(x2 + 31/3x + x2)}{(x + 31/3)(x2 - 31/3x + x2)}

So factors are (x - 31/3), (x2 + 31/3x + x2), (x + 31/3) and (x2 - 31/3x + x2).

Answer 3

(x^3 - 3)(x ^3 + 3)

Answer 4

3(2x - 9)