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Question
Divide of the following polynomial by synthetic division method and also by linear division method. Write the quotient and the remainder.
`(x^4 + 2x^3 +3x^2 + 4x + 5) ÷ (x + 2)`
Solution
Synthetic Division:
Dividend = `x^4 + 2x^3 +3x^2 + 4x + 5`
Divisor = x + 2
Opposite of 2 = −2
The coefficient form of the quotient is (1, 0, 3, −2).
∴ Quotient = x3 + 3x − 2 and Remainder = 9
Linear Method:
`x^4 + 2x^3 +3x^2 + 4x + 5`
`= x^3 (x + 2) + 3x (x + 2) - 6x + 4x + 5`
`= x^3 (x + 2) + 3x (x + 2) - 2x + 5`
`= x^3 (x + 2) +3x (x + 2) - 2 (x + 2) + 4 + 5`
`= (x + 2) xx (x^3 + 3x - 2) + 9`
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