In parts (a) through (d) below, for each polynomial function $f\left(x\right)$, the graph of $f\left(x\right)$ is shown. Based on this information, tell how many linear and quadratic factors the factored form of its equation should have and how many real and complex (non-real) solutions $f\left(x\right) = 0$ might have. (Assume a polynomial function of the lowest possible degree for each one.)

Example: f(x) at right will have three linear factors, therefore three real roots and no complex roots.

1. 

   Answer (a):

   There will be three linear factors (one is repeated), so the function will have two unique real roots and no complex roots.

2. 

   Answer (b):

   There will be one linear factor and one quadratic factor, so the function will have one real root and two complex roots.

3. 

   Answer (c):

   There will be four linear factors, so the function will have four real roots.

4. 

   Answer (d):

   There will be two linear factors and one quadratic factor, so the function will have two real roots and two complex roots.