Solving a Polynomial Inequality

Question

To solve the inequality $$x^3 - 4x^2 + 3x > 0$$, the expression is factored as $$x(x-1)(x-3) > 0$$. Based on this factorization, the proposed solution set is $$(-\infty, 0) \cup (1, 3)$$. Which of the following statements correctly identifies the error in this solution process and gives the correct solution set?

Accepted Answer

The error lies in the sign analysis of the factors; the correct solution set is $$(0,1) \cup (3,\infty)$$.

Answer

There is no mistake; the solution set $$(-\infty,0) \cup (1,3)$$ is correct.

Answer

The mistake is in the factorization; the expression should factor into a quadratic and a linear factor.

Answer

The error is due to treating the inequality as non-strict rather than strict.

Solving a Polynomial Inequality

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