Hello, nath_quam!
What do the graphs looks like and what are their key points?
$\displaystyle a)\;P(x) \:= \:x(3x+2)(x3)(x+2)$
$\displaystyle b)\; P(x) \:= \
1x)^3(x3)$
$\displaystyle a)\;P(x) \:=\:x(3x+2)(x3)(x+2)$ has xintercepts: $\displaystyle 2,\;\frac{2}{3},\;0,\;3$
As $\displaystyle x\to\infty,\;\;P(x) \to \infty$ . . . The graph rises to the right.
As $\displaystyle x\to\infty,\;\;P(x) \to \infty$ . . . The graph rises to the left.
You should be able to sketch the graph now . . .
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You can use the derivative to locate the exact positions
. . of the maximum and the two minimums.
$\displaystyle b)\;\;P(x)\:=\1x)^3(x3)$ has xintercepts: $\displaystyle 1,\;3$
The graph rises to the right and to the left.
We find that $\displaystyle (1,0)$ is an inflection point
. . and there is a minimum at $\displaystyle x = \frac{5}{2}$
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