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Question -

What must be subtracted from the polynomial f(x) = x4 + 2x3 – 13x2 – 12x + 21 so that the resulting polynomial is exactly divisible by x3 – 4x + 3 ?



Answer -


The resulting polynomial is exactly divisible by x2 – 4x + 3
Remainder = 0
=> 2x -3 – k = 0
=> k = 2x – 3
(2x – 3) must be subtracted

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