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8-105.

Make a sketch of a graph $p(x)$ so that $p(x) = 0$ would have the indicated number and type of solutions.

$5$ real solutions
Hint (a):
Your graph should have five $x$ -intercepts.

$3$ real and $2$ complex
Hint (b):
Draw a graph with three $x$ -intercepts that when shifted vertically would have five $x$ -intercepts.

$4$ complex
Hint (c):
Draw a graph with no $x$ -intercepts. But, when it is shifted down it should have four $x$ -intercepts.

$4$ complex and $2$ real

For parts (a) through (d), what is the lowest degree each function could have?
Hint (e):
The degree needs to be at least as high as the number of solutions.

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