First name:   Last name:

1.  The solution to the equation \(x^3 - 3x^2 = 4x\) is

a.  \(x = 0, 4\)

b.  \(x = -1, 0, 1\)

c.  \(x = -1, 0 , 4\)

d.  \(-1 \leq x \leq 1\)

e.  \(x = 4\)

2.  The solution to the equation \(x^2 - 4 = 2x\) is

a.  \(x = 2, 4\)

b.  \(x = 1+\sqrt{20}, x = 1-\sqrt{20}\)

c.  \(x = 1+\sqrt{5}, x = 1-\sqrt{5}\)

d.  \(x = 1+\sqrt{3}i, x = 1-\sqrt{3}i\)

e.  No solutions

3.  The solution to the inequality \(x^2 + 2 < x\) is

a.  \(x = 1+\sqrt{7}, x=1-\sqrt{7}\)

b.  \(x = 1+\sqrt{5}, x=1-\sqrt{5}\)

c.  \(x = \frac{1+\sqrt{7}}{2}, x=\frac{1-\sqrt{7}}{2}\)

d.  \(\frac{1+\sqrt{5}}{2}, x=\frac{1-\sqrt{5}}{2}\)

e.  No solutions

4.  The solution to the inequality \(x^2 \geq 2x + 3\) is

a.  \(x \geq 3\)

b.  \(x \geq 3\) or \(x \leq -1\)

c.  \(x \geq 3\) or \(x \geq -1\)

d.  \( -1 \leq x \leq 3\)

e.  \(x \leq -1\) and \(x \leq 3\)

5.  Solve \(x^3 = x\).

a.  \(x=-1, x = 1\)

b.  \(x = -1, x = 0, x = 1\)

c.  \(x = -1, x= 0, x = 1, x = 2\)

d.  \(x = 1\)

e.  no solutions