What is the product of the binomials $(2x+3)(x+4)$ when expanded by FOIL?

Factor the trinomial $15x^2+20x+5$ by first extracting the GCF. What is the final factored form?

Use the AC method to factor $6x^2+17x+5$.

A manufacturing model predicts profit: $P\left(t\right)=2t^2-11t-21$ dollars, where $t$ is in thousands of units. Factor $P\left(t\right)$ completely to identify production thresholds (in thousands of units) and interpret the roots.

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