$$p(t)=2t+3$$ $$r(t)=t^2+1$$ $$s(t)=2t^2-5$$

The polynomial functions $p, r,$ and $s$ are defined above. Which of the following is equivalent to $3p(t)-2r(t)-4s(t)$ ?

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$$3p(t)-2r(t)-4s(t)$$ $$=3(2t+3)-2(t^2+1)-4(2t^2-5)$$ $$=6t+9-2t^2-2-8t^2+20$$ $$=\boxed{-10t^2+6t+27}$$

We can try substituting an arbitrary value of $t$. For example, substituting $t=0$:

$$3p(t)-2r(t)-4s(t)$$ $$3p(0)-2r(0)-4s(0)$$ $$=3(3)-2(1)-4(-5)$$ $$=9-2+20$$ $$= 27$$

Browsing the answer choices, only the last option evaluates to $27$ when $t=0$.