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Question
Divide and write the quotient and the remainder.
(a4 − a3 + a2 − a + 1) ÷ (a3 − 2)
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Solution
(a4 − a3 + a2 − a + 1) ÷ (a3 − 2)
a - 1
`a^3 - 2")"overline(a^4 + a^3+a^2-a +1)`
a4 + 0a3 + 0a2 - 2a
- - - +
-a3 + a2 + a + 1
-a3 + 0a2 + 0a + 2
+ - - -
a2 + a - 1
So, quotient = a - 1 and remainder = a2 + a - 1
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