How do you factor #6x^3 - 36x^2 - 162x#?

Answer 1

#6x^3-36x^2-162x = 6x(x^2-6x-27)#

#= 6x(x^2-(9-3)x-(9xx3)) = 6x(x-9)(x+3)#

Having separated the common #6x# factor out, it remained to try to find a factorization of #27# into two factors whose difference was #6#. There are not many choices to try and the pair #9, 6# works.

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Answer 2

Eva Abramson

To factor 6x^3 - 36x^2 - 162x, first, identify the greatest common factor (GCF), which is 6x. Then, divide each term by the GCF:

6x^3 ÷ 6x = x^2 -36x^2 ÷ 6x = -6x -162x ÷ 6x = -27

Now rewrite the expression using the GCF:

6x(x^2 - 6x - 27)

Next, factor the quadratic expression inside the parentheses:

x^2 - 6x - 27 = (x - 9)(x + 3)

Therefore, the factored form of 6x^3 - 36x^2 - 162x is 6x(x - 9)(x + 3).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.