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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.
`(2m^2 - 3m + 10) ÷ (m - 5)`
Solution
Synthetic Division:
Dividend = `2m^2 - 3m + 10`
Divisor = m - 5
Opposite of −5 = 5
The coefficient form of the quotient is (2, 7).
∴ Quotient = 2m + 7 and Remainder = 45
Linear Method:
`2m^2 - 3m + 10`
`= 2m(m - 5) + 10m - 3m + 10`
`= 2m(m - 5) + 7 (m - 5) + 35 + 10`
`=(m - 5) xx (2m + 7) + 45`
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