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

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

Real factor:

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

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

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

**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?