If P(x)=x3−3x2−4x, 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)=x3−3x2−4xGiven=x(x2−3x−4)Factor out x=x(x−4)(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(0−4)(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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