Key to the Practice Midterm

Problem 1:  Roots:  -2 (multiplicity 2), sqrt(2), -sqrt(2)

Factorization:  (x + 2)²(x - sqrt(2))(x + sqrt(2))

 Problem 2:  Left up, Right up, at x = -2 it looks like a parabola, at x = +- sqrt(2) it looks like a line.

Problem 3:  Missing Equation

Problem 4:  (-infinity,-1.8) u (-.45,1) u (1.25, infinity)

Problem 5:  

A.  1 positive real root, 3 or 1 negative real root

B.  +-1, +-2, +-5, +-10, +-1/2, +-1/4, +-5/2, +- 5/4

C.   -2 + 2i and -2 - 2i are both roots by the conjugate root theorem, there is exactly one real positive root by DRS, this leaves only one root left by the fundamental theorem of algebra which must be a negative real root by DRS.

Problem 6:  

-1/4 (x + 3)³(x² - 2x + 2)(x² - 2)