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Prime Factors

One of the fa...

Question

One of the factors of $P (x) = x^{4} - x^{3} - 19 x^{2} + 49 x - 30$ is :

(x + 1)

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(x - 1)

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(x + 2)

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(x - 2)

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Solution

The correct option is C $(x - 1)$
Let $f (x) = x^{4} - x^{3} - {19 x}^{2} + 49 x - 30$
We find the first factor generally by hit and trial method
Put $x = 1$
$f (1) = 1 - 1 - 19 + 49 - 30 = 0$
So $(x - 1)$ is a factor of $f (x)$ .
So option $B$ is correct.

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