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How do you factor #(2x - 3)^3 - 27#?

Answer 1

Ethan Adkins

Factoring #(2x-3)^3 -27#

Consider a related problem: Find the solutions for #(2x-3)^3 -27 = 0#

#(2x-3)^3 = 27#

#(2x-3)^3 = 3^3#

#2x-3 = 3#

#x=3#

So #(x-3)# is a factor of #(2x-3)^3-27#

Using synthetic division we can determine that #(2x-3)^3-27 = (x-3)(8x^2-12x+18)#

We can extract a common factor of #(2)# from this final factor #(2x-3)^3-27 = (x-3)(2)(4x^2-6x+9)#

Examining the discriminant of #(4x^2-6x+9)# reveals that there are no further factors.

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Answer 2

Isaiah Anthony

To factor the expression (2x - 3)^3 - 27, you can use the difference of cubes formula, which states that a^3 - b^3 = (a - b)(a^2 + ab + b^2). Applying this formula to the given expression, you get ((2x - 3) - 3)((2x - 3)^2 + (2x - 3)(3) + 3^2). Simplify each part of the factored expression to get the final result.

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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.