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Question

Using factor theorem, show that g(x) is a factor of p(x), when p(x)=x4x212, g(x)=x+2.

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Solution

The given polynomial is
p(x)=x4x212
and g(x)=x+2

Now,
g(x)=0
x+2=0
x=2

If, (x+2) is a factor of p(x), then p(2)=0
Putting, x=2
p(2)=(2)4(2)212
=16412
=0

Hence, (x+2) is a factor of p(x).

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