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How do you factor: #y= 2x^7 - 32x^3 #?

Answer 1

Nathan Axel

#y=2x^3(x^4-16)#

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Answer 2

Hazel Anglin

To factor the expression (y = 2x^7 - 32x^3), you can first factor out the greatest common factor, which is (2x^3):

(y = 2x^3(x^4 - 16))

Next, you can recognize that (x^4 - 16) is a difference of squares, which can be factored as ((x^2)^2 - (4)^2):

(y = 2x^3((x^2 - 4)(x^2 + 4)))

Now, (x^2 - 4) is another difference of squares, so it factors as ((x - 2)(x + 2)):

(y = 2x^3((x - 2)(x + 2)(x^2 + 4)))

So, the factored form of (y = 2x^7 - 32x^3) is (y = 2x^3(x - 2)(x + 2)(x^2 + 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.