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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 - 3y^2 + 5y - 1) ÷ (y - 1)`
Solution
Synthetic Division:
Dividend = `y^3 - 3y^2 + 5y - 1`
Divisor = y − 1
Opposite of −1 = 1
The coefficient form of the quotient is (1, −2, 3).
∴ Quotient = y2 − 2y + 3 and Remainder = 2
Linear Method:
`y^3 - 3y^2 + 5y - 1`
`= y^2 (y - 1) + y^2 - 3y^2 + 5y - 1`
`= y^2 (y - 1) - 2y (y - 1) -2y +5y - 1`
`= y^2 (y - 1) - 2y (y - 1) + 3(y -1) + 3 - 1`
`= (y - 1) (y^2 - 2y + 3) + 2`
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