APFIVE Solving a Polynomial Inequality
A researcher attempts to solve the inequality
$$x^3-4*x^2+3*x>0$$
by factoring it as
$$x*(x-1)*(x-3)>0$$ and concludes that the solution set is
$$(-\infty,0) \cup (1,3).$$
Identify the mistake in this process and state the correct solution set.
A
The mistake is in the factorization; the expression should factor into a quadratic and a linear factor.
B
There is no mistake; the solution set $$(-\infty,0) \cup (1,3)$$ is correct.
C
The error is due to treating the inequality as non-strict rather than strict.
D
The error lies in the sign analysis of the factors; the correct solution set is $$(0,1) \cup (3,\infty)$$.
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