What must be added to the polynomia...
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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
Maths
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The given polynomial is ( f(x)=x^{4}+2 x^{3}-2 x^{2}+x-1 . ) To make this polynomial exactly divisible by ( x^{2}+2 x-3, ) let us add ( p ) then ( x^{4}+2 x^{3}-2 x^{2}+x-1+p ) is exactly divisible by ( x^{2}+2 x-3 ) ( left.x^{2}+2 x-3right) x^{4}+2 x^{3}-2 x^{2}+x-1+pleft(x^{2}right. ) ( x^{4}+2 x^{3}-3 x^{2} ) ( frac{-x^{2}-x+}{x^{2}+x-1+p} ) For remainder to be zero, ( x^{2}+2 x-3=x^{2}+x-1+p ) So, ( p=x-2 ) So, ( x-2 ) to be added to make the polynomial divisible by ( x^{2}+2 x-3 )
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