Thursday, March 22, 2018

College Algebra, Chapter 4, 4.2, Section 4.2, Problem 28

Factor the polynomial P(x)=x3+2x28x and use the factored form to find the zeros. Then sketch the graph.

P(x)=x3+2x28x=x(x2+2x8)Factor out x=x(x+4)(x2)Simplify

Since the function has an odd degree of 3 and a positive leading coefficient, its end behaviour is y as x and y as x. To find the x intercepts (or zeros), we set y=0.
0=x(x+4)(x2)

By zero product property, we have
x=0,x+4=0 and x2=0

Thus, the x-intercept are x=0,4 and 2

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