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What must be added to the polynomial f(x)=x+ +2x2_2x2+x-so that the resulting polynomial is exactly divisible by x2 + 2x - 3?

JEE/Engineering Exams
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The given polynomial is f(x) = x4 + 2x3 - 2x2 + x - 1. To make this polynomial exactly divisible by x2 + 2x - 3, let us add p then x4 + 2x3 - 2x2 + x-1+p is exactly divisible by x2 + 2x-3. x x + 2x - 3) x + 2x - 2x + x-1+p 4 3 2 x + 2x - 3x - - + x+x-1+p For remainder to be zero, x2 + 2x -3 = x2 + x-1+p So,p=x-2, So, X-2 to be added to make the polynomial divisible by x2 + 2x-3.
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