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Question 125

If (x - 2) is a factor of $$p(x^2 + 4)$$. where p(x) is a polynomial. then a factor of p(x) is

Solution

If (x-2) is a factor of $$p\left(x^2+4\right)$$, it means that at x = 2, $$p\left(x^2+4\right)$$ = 0
That is, $$p\left(2^2+4\right)=0$$ i.e. p(8) = 0

This is equivalent to saying that whatever polynomial function p(x) is, (x-8) is a factor of p(x) as we can see that p(8) = 0

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