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प्रश्न
Find the quotient and the remainder when :
a3 − 5a2 + 8a + 15 is divided by a + 1. verify your answer.
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उत्तर
`"a"+1) overline("a"^3-5"a"^2+8"a"+15)("a"^2-6"a"+14`
a3 + a2
− −
−6a2 + 8a + 15
−6a2 − 6a
+ +
14a + 15
14a + 14
1
∴ Quotient = a2 − 6a + 14 and reminder = 1
Verification :
Dividiend = Quotient × Divisor + Reminder
= (a2 − 6a + 14) × (a + 1) + 1
= a3 − 6a2 + 14a + a2 − 6a + 14 + 1
= a3 − 5a2 + 8a + 15 which is given
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