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Question

(x + 2) is a factor of x4 - 16.


A

True

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B

False

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Solution

The correct option is A

True


x4 - 16 = (x2 - 4) (x2 + 4)........... [using a2b2 = (a + b)(a - b)]

(x2 - 4) is further factorable using the same formula.

So we get, (x2 - 4) = (x + 2)(x - 2)

This shows that, (x + 2) is a factor of x4 - 16


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