A student factors $16x^2-24x+9$ as $(4x-3{)}^2$. Evaluate whether this is correct and justify.

Incorrect — FOIL yields $16x^2-18x+9$, so the student's middle term is off by $-6x$

Incorrect — the correct factorization is $(8x-3)(2x-3)$ because you must distribute coefficients evenly

Correct — the trinomial is a perfect square, and the factors expand to give $16x^2-24x+9$ when FOIL is applied

Cannot be determined without computing the discriminant first to see if roots are rational