What must be added to the polynomial f/x )= x 4 2x 2 2x 2 x 1 so that resulting polynomial is exactly divisible by x 2 2x 3?
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x - 2 Show
By division Algorithm we have, From above relation we got that if we add -r(x) to f(x) then resulting polynomial is divisible by g(x). Now find the remainder when f(x) is divisible by g(x), r(x) = - x + 2 Therefore, - r(x) = x - 2 has to be added so that resulting polynomial is divisible by g(x).
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What must be added to x 4 2x 3 2x 2 x 1 so that result is exactly divided by x 2 2x 3?∴ x – 2 has to be added to x4 + 2x3 – 2x2 + x – 1 so that the resulting polynomial is exactly divisible by x2 + 2x -3.
What must be added to the polynomial f/x )= x⁴ 2x³ 2x² x 1 so that the resulting polynomial is exactly divisible by G x )= x² 2x 3?DIVISION PROCESS is in the attachment.
Now the polynomial f(x) = x⁴ + 2x³ -2x² + x -1 will be exactly divisible by g(x) = x² + 2x + 3, when reminder is zero. So to make the remainder 0 , x+2 is to be added in f(x) .
What must be added to the polynomial?Thus, if we add - r(x) to f(x), then the resulting polynomial is divisible by g(x). Let us now find the remainder when f(x) is divided by g(x). Hence, we should add - r(x) = x - 2 to f(x) so that the resulting polynomial is divisible by g(x).
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