Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
(i) p(x) = x³ - 3x² + 5x - 3, g(x) = x² - 2
(ii) p(x) = x⁴ - 3x² + 4x + 5, g(x) = x² + 1 - x
(iii) p(x) = x⁴ - 5x + 6, g(x) = 2 - x²

(i)x-3
x²-2)
x³ - 3x² + 5x - 3
x³ -2x

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-3x² + 7x - 3
-3x² +6

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7x - 9
Quotient = x - 3
Remainder = 7x - 9
(ii)x²+x-3
x²-x+1)
x⁴ - 3x² + 4x + 5
x⁴ - x³ + x²

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x³ - 4x² + 4x + 5
x³ - x² + x

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-3x² + 3x + 5
-3x² + 3x - 3

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8
Quotient = x² + x - 3
Remainder = 8
(iii)-x²-2
2-x²)
x⁴ + 0x³ + 0x² - 5x + 6
x⁴ -2x²

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2x² - 5x + 6
2x² -4

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-5x + 10
Quotient = -x² - 2
Remainder = -5x + 10