"Your friend is using Descartes's Rule of Signs to find the number of negative real roots of x^3 + x^2 + x + 1 = 0. Describe and correct the error."
"P(-x) = (-x)^3 +(-x)^2 + (-x) +1
= -x^3 - x^2 - x +1"
"Because there is only one sign change in P(-x), there must be one negative real root."
Answer: "Because there are three sign changes in P9-x), there must be three and/or one negative real root."