Divide the polynomial $p (x) = x^{3} - 3 x^{2} + 5 x - 3$ by the polynomial $g (x) = x^{2} - 2$ . Find the quotient and remainder.

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Solution

Given:-
$p (x) = x^{3} - 3 x^{2} + 5 x - 3$
$g (x) = x^{2} - 2$
$p (x) \div g (x)$
$(x^{3} - 3 x^{2} + 5 x - 3) \div (x^{2} - 2)$
$\frac{x^{3} - 3 x^{2} + 5 x - 3}{x^{2} - 2} = (x - 3) + \frac{(7 x - 9)}{(x^{2} - 2)}$
Quotient $= (x - 3)$
Remainder $= (7 x - 9)$

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

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Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

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

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

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

Question 1 (i)
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

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

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