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Question
Find the quotient and the remainder when f(x) = x4 – 5x + 6 is divided by g(x) = 2 – x2.
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Solution
f(x) as x4 + 0x3 + 0x2 – 5x + 6 and g(x) as – x2 + 2
– x2 – 2
`-x^2 + 2")"overline(x^4 + 0x^3 + 0x^2 - 5x + 6)`
x4 – 2x2
– +
2x2 – 5x + 6
2x2 – 4
– +
–5x + 10
Quotient q(x) = – x2 – 2
Remainder r(x) = –5x + 10
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