perplexus.info :: Just Math : Coefficient Determination

Coefficient Determination (Posted on 2015-10-14)

p₀(x) = x³+ 313x² - 77x - 8, and:
p_n(x) = p_n-1(x-n).

Determine the coefficient of x in p₂₀(x)

No Solution Yet Submitted by K Sengupta

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Possible solution

| Comment 1 of 3

p₁(x) = (x-1)³+ 313(x-1)² - 77(x-1) - 8

p₂(x) = (x-3)³+ 313(x-3)² - 77(x-3) - 8

p₃(x) = (x-6)^{3 etc}

Oh it's just triangular numbers. The 20th is 210.

p₂₀(x) = (x-210)³+ 313(x-210)² - 77(x-210) - 8

The x coefficient would be

3*210^2 + 313*2*-210 - 77 = 763

Posted by Jer on 2015-10-14 13:02:39

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