Tuesday, October 25, 2016

College Algebra, Chapter 4, 4.2, Section 4.2, Problem 38

Factor the polynomial P(x)=x42x3+8x16 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=x42x3+8x160=x42x3+(8x16)Group terms0=x3(x2)+8(x2)Factor out x20=(x3+8)(x2)Factor out x3+8



By zero product property, we have
x3+8=0 and x2=0

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

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