what must be added to the polynomial 5 x power 4 + 66 x cube minus 13 x square - 44 X + 7 so that the resulting polynomial is divisible by X square + 4 x + 3
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Sol: Given polynomial x3 - 3x2 - 12x + 19 x2 + x - 6 ) x3 - 3x2 - 12x + 19 ( x - 4 x3 + x2 - 6x ( substract) ---------------------------- - 4x2 - 6x + 19 - 4x2 - 4x + 24 ( substract) ---------------------------- - 2x - 5 Here remainder is - 2x - 5 . 2x + 5 must be added to x3 - 3x2 - 12x + 19, so that result is exactly divisible by x2 + x - 6.
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