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Question
Divide the following polynomial by synthetic division method and also by linear division method. Write the quotient and the remainder.
`(y^3 - 216) ÷ (y - 6)`
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Solution
Synthetic Division:
Dividend = `y^3 - 216 = y^3 + 0y^2 +0y -216`
Divisor = y − 6
Opposite of −6 = 6
The coefficient form of the quotient is (1, 6, 36).
∴ Quotient = y2 + 6y + 36 and Remainder = 0
Linear Method:
`y^3 - 216`
`= y^2 (y - 6) + 6y^2 -216`
`= y^2 (y - 6) + 6y(y - 6) + 36 y - 216`
`= y^2 (y - 6) + 6y (y - 6) + 36 (y -6) +216 - 216`
`= y^2 (y - 6) + 6y(y - 6) + 36 (y -6)`
`= (y - 6) xx (y^2 + 6y + 36)`
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