Graph the polynomial p(x) = (x-3)(x+2)(x+5).

We first start by plotting the roots - which are 3, -2, and -5.



Now we see if the coefficient in front of the x³ is positive or negative. When we expand it, we get:
x³ + 4x² - 11x - 30 therefore it is positive which implys the graph will go from bottom left to upper right.



Since it is easy to substitute the value x = 0, we see that there is another point (0,-30) that will help in the plotting of the graph. Using this, we sketch the graph to be



But the graph might also look like this



Since it is only a sketch, both of these are a valid answer.

Graph the polynomial p(x) = (-x+2)(x²+5).

First we plot the real roots. In this case there is only one, it being 2.



When expand the polynomial we get -x³.+.2x².-.5x.+.10. Therefore the graph goes from upper left to lower right.



Again by subtituting the value x = 0, we get the point (0,10). Combining this bit of information, we get a sketch of the graph to look like



Another sketch is:



And still another sketch could be



Again, all are valid SKETCHES. With the information that we have, it is not possible to determine the shape of the graph any more then what we have done.

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