How do you factor #6x^3-48#?

Answer 1

#6(x-2)(x^2 + 2x + 4)#

To factor, we have to find the GCF, or Greatest Common Factor. This means the largest factor that both expressions have.

Therefore, the GCF is #6#. So when we factor it becomes: #6(x^3 - 8)#

We can still factor this further.

#(x^3 - 8)# is in the form #a^3 - b^3#, which factors down to #(a-b)(a^2 + ab + b^2)#

Therefore, that becomes: #(x-2)(x^2 + 2x + 4)#

So the completely factored answer is: #6(x-2)(x^2 + 2x + 4)#

Hope this helps!

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Answer 2

Eva Abramson

To factor the expression (6x^3 - 48), first, factor out the greatest common factor, which is 6. Then, factor out the difference of cubes formula, (a^3 - b^3), where (a = x) and (b = 2):

(6x^3 - 48)
(= 6(x^3 - 8))
(= 6(x - 2)(x^2 + 2x + 4))

So, the factored form of (6x^3 - 48) is (6(x - 2)(x^2 + 2x + 4)).

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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.