# Will anyone help me with this?

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 $$f(x)= A(x-1)^{4} + B(x-1)^{3} + C(x-1)^{2} + D(x-1) +E$$

Note by Sopheak Seng
4 years, 3 months ago

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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.

- 4 years, 3 months ago

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 $$2(x+1)^5 \ldots$$.

- 4 years, 3 months ago