If $a x^{3} + 4 x^{2} + 3 x - 4 a n d x^{3} - 4 x + a$ leaves same remainder when divided by (x - 3) the value of -a is

composite number

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prime number

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neither composite nor prime

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an integer

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Solution

The correct option is C neither composite nor prime
$p (x) = a x^{3} + 4 x^{2} + 3 x - 4$
$g (x) = x^{3} - 4 x + a$
remainder when $p (x)$ is divided by $(x - 3) = p (3) = 27 a + 36 + 9 - 4 = 27 a - 41$
remainder when $g (x)$ is divided by $(x - 3) = g (3) = 27 - 12 + a = 15 + a$
so $27 a - 41 = 15 + a$
$a = \frac{56}{41}$

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Similar questions

If the polynomials $a x^{3} + 4 x^{2} + 3 x - 4 a n d x^{3} - 4 x + a$ leave the same remainder when divided by (x - 3), find the value of a.

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