Apply the division algorithm to find the quotient and remainder on dividing f(x) by g(x) as given below:
$f (x) = x^{4} - 5 x + 6, g (x) = 2 - x^{2}$

Q = x^{2} - 2, R = - 5 x + 2

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Q = - x^{2} - 2, R = - 5 x + 10

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Q = x^{2} - 5, R = 2 - x

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Q = x^{2} + 6, R = 2 - 2 x

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Solution

The correct option is B $Q = - x^{2} - 2, R = - 5 x + 10$

Let us divide $f (x) = x^{4} - 5 x + 6$ by $g (x) = 2 - x^{2}$ as shown in the above image.

Hence, the quotient is $q (x) = - x^{2} - 2$ and the remainder is $r (x) = - 5 x + 10$ .

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f (x) = x^{4} - 5 x + 6

g (x) = 2 - x^{2}

p (x)

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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}

Find the quotient and the remainder when

$f (x) = x^{4} - 5 x + 6$ is divided by $g (x) = 2 - x^{2}$

f (x) = x^{3} - 3 x^{2} + 5 x - 3

x^{2}

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