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A function is given \(f(x)= 2x^{4} - 3x^{3} + 4x^{2} - 5x +6\), calculate the sum of \(S= A+B+C+D+E\) , if \(f(x)= A(x-1)^{4} + B(x-1)^{3} + C(x-1)^{2} + D(x-1) +E\)

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Make the substitution x = z - 1 and expand f(x) to get 2z^5 + 5z^4 + 7z^2 + 2z + 4. Hence, S = 2 + 5 + 7 + 2 + 4 = 20.

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Wouldn't we take \( x = z + 1 \). Because If \( x = z - 1 \), we'd have \( x + 1 = z \) and the f(x) you got would be \( 2(x+1)^5 \ldots \).

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`*italics*`

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TopNewestMake the substitution x = z - 1 and expand f(x) to get 2z^5 + 5z^4 + 7z^2 + 2z + 4. Hence, S = 2 + 5 + 7 + 2 + 4 = 20.

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Wouldn't we take \( x = z + 1 \). Because If \( x = z - 1 \), we'd have \( x + 1 = z \) and the f(x) you got would be \( 2(x+1)^5 \ldots \).

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