For a polynomial, dividend is $x^{4} + 4 x - 2 x^{2} + x^{3} - 10$ , quotient is $x^{2} + 3 x - 3 x^{2} + 4 x + 12$ and remainder is $14$ , then divisor is equal to

x^{2} + 2

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x^{2} - 2

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x + 2

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None of these

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Solution

The correct option is B None of these
$p (x) = x^{4} + 4 x - 2 x^{2} + x^{3} - 10$ and $q (x) = x^{2} + 3 x - 3 x^{2} + 4 x + 12$ and $r (x) = 14$
$p (x) - 14$ is not divisible by $(x^{2} + 2), (x^{2} - 2), (x + 2)$
hence correct option is (D)

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Similar questions

If dividend = $x^{4} + x^{3} - 2 x^{2} + x + 1$ , divisor = $x - 1$ and remainder = 2. Find the quotient q(x)

x^{4} + x^{3} - 2 x^{2} + x + 1

= x - 1

= 2

x^{2} + 1 - x

x^{4} - 3 x^{2} + 4 x + 5

p (x)

g (x)

p (x) = x^{3} - 3 x^{2} + 5 x - 3, g (x) = x^{2} - 2

p (x) = x^{4} - 3 x^{2} + 4 x + 5, g (x) = x^{2} + 1 - x

p (x) = x^{4} - 5 x + 6, g (x) = 2 - x^{2}

$If the dividend = x^{4} + x^{3} - 2 x^{2} + x + 1, divisor = x - 1 and remainder = 2, then find the quotient q(x) .$

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