APFIVE When evaluating $$\lim_{x\to \infty} \frac{3x^2 - 2x + 1}{5x^2 + 4}$$, a student’s procedure involves dividing the numerator and denominator by $$x$$. This step, combined with another error, leads to the correct answer of $$\frac{3}{5}$$. Which statement describes the primary flaw in the student’s method?
The mistake is in expanding the polynomials rather than factoring them first.
There is no mistake because the limit still evaluates to $$\frac{3}{5}$$.
The error is in using polynomial long division instead of direct cancellation.
The error is in dividing by the wrong power of $$x$$; since the highest power in the expression is $$x^2$$, both numerator and denominator should be divided by $$x^2$$ to simplify correctly.
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