**Problem : **
How many variations are in the function
*f* (*x*) = *x*
^{6} -6*x*
^{4} +2*x*
^{2} + 2*x* - 7
?

**Problem : **
How many positive and negative real roots might the function
*f* (*x*) = 2*x*
^{3} -3*x*
^{2} - 4*x* + 1
have?

**Problem : **
What are the possible rational roots of
*f* (*x*) = *x*
^{3} -4*x*
^{2} + 3*x* - 6
? Use
Descartes' Rule of Signs and the Rational Root Theorem.

**Problem : **
Find all real roots of
*x*
^{3} +
*x*
^{2} - 4*x* - 2
.

**Problem : **
Find all real roots of
*x*
^{4} +5*x*
^{3} - 15*x* + 9
.