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How do you factor #4x^3 - 32= 0#?

Answer 1

Julia Adams

#x = 2#

#4x^3 - 32 = 0#

Factor out the #4#: #4(x^3 - 8) = 0#

Divide both sides by #color(blue)4#: #(4(x^3 - 8))/color(blue)4 = 0/color(blue)4#

#x^3 - 8 = 0#

Add #color(blue)8# to both sides of the equation: #x^3 - 8 quadcolor(blue)(+quad8) = 0 quadcolor(blue)(+quad8)#

#x^3 = 8#

Take the cube root of both sides: #root(3)(x^3) = root(3)(8)#

#x = 2#

Hope this helps!

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Answer 2

Genesis Allen

To factor (4x^3 - 32 = 0), first, factor out the greatest common factor, which is 4. Then, use the difference of cubes formula, (a^3 - b^3 = (a - b)(a^2 + ab + b^2)).

So, (4x^3 - 32 = 4(x^3 - 8)), and (x^3 - 8) can be further factored as ((x - 2)(x^2 + 2x + 4)).

Therefore, the factored form of (4x^3 - 32 = 0) is (4(x - 2)(x^2 + 2x + 4) = 0).

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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.