Monday, August 20, 2018

College Algebra, Chapter 4, Chapter Review, Section Review, Problem 40

If P(x)=x33x24x, then

a.) Find all zeros of P, and state their multiplicities.

b.) Sketch the graph of P.



a.) To find the zeros of P, we factor P to obtain


P(x)=x33x24xGiven=x(x23x4)Factor out x=x(x4)(x+1)Factor the quadratic function



It shows that the function has zeros of 0,4 and 1. And all the zeros have multiplicity of 1.

b.) To sketch the graph of P, we must know first the intercepts of the function. The values of the x intercepts are the zeros of the function, that is 0,4 and 1. To determine the y intercept, we set x=0 so, P(0)=0(04)(0+1)=0

The y intercept is .

Since the function has an odd degree and a positive leading coefficient, then its end behavior is y as x and y as x. Then, the graph is

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