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How do you factor by grouping #2x^3+12x^2-5x-30#?

Answer 1

Avery Alexander

#(x+6)(\sqrt2x+\sqrt5)(\sqrt2x-\sqrt5)#

Given polynomial:

#2x^3+12x^2-5x-30#

#=2x^2(x+6)-5(x+6)#

#=(x+6)(2x^2-5)#

#=(x+6)((\sqrt2x)^2-(\sqrt5)^2)#

#=(x+6)(\sqrt2x+\sqrt5)(\sqrt2x-\sqrt5)#

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Answer 2

Nathan Axel

To factor by grouping the expression (2x^3 + 12x^2 - 5x - 30), you can first group the terms in pairs:

Group 1: (2x^3) and (12x^2) Group 2: (-5x) and (-30)

Then, factor out the greatest common factor from each pair:

From Group 1: (2x^2(x + 6)) From Group 2: (-5(x + 6))

Now, you can see that both terms have a common factor of ((x + 6)). Factor out this common factor:

((x + 6)(2x^2 - 5))

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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.