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black spots on the soles of feet - Coaching Toolbox

📅 May 5, 2026 👤 scraface

May 05, 2026

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Question: Let $ p(x) $ be a polynomial such that
p(x) = x^3 - 3x^2 + 5x - 7,
and define $ q(x) = p(x+1) $. What is the coefficient of $ x^2 $ in $...
and $ q(x) = p(x+1) $. To find the coefficient of $ x^2 $ in $ q(x) $,...
q(x) = p(x+1) = (x+1)^3 - 3(x+1)^2 + 5(x+1) - 7.
Now expand each term:
-3(x+1)^2 = -3(x^2 + 2x + 1) = -3x^2 - 6x - 3, \\
5(x+1) = 5x + 5.
Adding all terms:
q(x) = x^3 + 3x^2 + 3x + 1 - 3x^2 - 6x - 3 + 5x + 5 - 7.

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