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Divide 3-x+2x^(2) by (2-x) and verify ...

Divide `3-x+2x^(2) ` by (2-x) and verify the division algorithm.

Text Solution

Verified by Experts

First we write the terms of dividend and divisor in decreasing order of their degrees and then perform the division as shown below.

Clearly, degree (9) =`0 lt ` degree (-x+2).
`:. ` quotient = (-2x-3) and remainder = 9
`rArr` (quotient `xx` divisor) + remainder
` = (-2x-3)(-x+2)+9`
` = 2x^(2) - 4x + 3x - 6 +9`
` = 2x^(2) - 4x + 3x - 6 + 9`
` = 2x^(2) - x+3`
= dividend.
Thus, (quotient `xx` divisor)+ remainder = dividend.
Hence, the division algorithm is verified.
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