Sunday, July 28, 2019

College Algebra, Chapter 4, 4.2, Section 4.2, Problem 40

Factor the polynomial P(x)=x62x3+1 and use the factored form to find the zeros. Then sketch the graph.
Since the function has an even degree of 4 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=x62x3+10=w22w+1Let w=x30=(w1)2Perfect Squarew=1Substitutew=x3x3=1



Thus, the x-intercept are x=1

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