**Problem : **
What is the multiplicity of each root of *P*(*x*) = (*x* - 3)^{2}(*x* - 5)^{3}(*x* + 1)?

*x* = 3 has multiplicity 2.

*x* = 5 has multiplicity 3.

*x* = - 1 has multiplicity 1.

**Problem : **
If *x* = 2 - 7*i* is a root of *P*(*x*), what is another root? Name one real factor
of *P*(*x*).

Root:

*x* = 2 + 7*i*.

Real factor:

*x*^{2} - 4*x* + 53.

**Problem : **
If *x* = 4 - 3*i* is a root of *P*(*x*) = *x*^{3} -12*x*^{2} + 57*x* - 100, factor *P*(*x*)
completely.

*P*(*x*) = (*x* - 4 + 3*i*)(*x* - 4 - 3*i*)(*x* - 4)
**Problem : **
If 2 + 5*i* is a root of *P*(*x*) = *x*^{3} -5*x*^{2} + 33*x* - 29, factor *P*(*x*)
completely.

*P*(*x*) = (*x* - 2 + 5*i*)(*x* - 2 - 5*i*)(*x* - 1).

**Problem : **
How many complex roots foes 4*x*^{5} +3*x*^{4} -2*x*^{3} + 1 have?

5.

**Problem : **
How many complex roots does 3*x*^{4} +4*ix*^{3} +3*ix*^{2} +4*x*^{2} - 5*ix* - 2*x* + 5*i* - 7
have?

4.