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Divide 4x^(3)-11x^(2)+7x-2 by 1+x-x^(2) ...

Divide `4x^(3)-11x^(2)+7x-2` by `1+x-x^(2)` and verify the division algorithm.
Note
Always write the divided and divisor in standard form i.e., decreasing order of the variable.

Text Solution

Verified by Experts

Here, dividend `=4x^(2)-11x^(2)+7x-2`
divisor `=1+x-x^(2)=-x^(2)+x+1`

`:. ` quatient =4x-7 and remainder =18x+5
Now, `"quatient"xx"divisor" +"remainder"=(-4x-7)(-x^(2)+x+1)+(18x+5)`
`=4x^(2)+3x^(2)+7x-2`=divised `" "` Hence Verified.
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