Question

Use the remainder theorem to determine the remainder when 3t²+5t-7 is divided by t-5

Answer 1

$f(t)=3t^2+5t-7\implies f(5)=3(5)^2+5(5)-7=93$

which means the remainder upon dividing $f(t)$ by $t-5$ is 93.

This is because we can write

$\dfrac{f(t)}{t-5}=q(t)+\dfrac{r(t)}{t-5}$

where $q(t)$ is the quotient and $r(t)$ is the remainder. Multiplying both sides by $t-5$, then evaluating at $t=5$ makes the $q(t)$ term vanish, leaving the remainder:

$f(t)=q(t)(t-5)+r(t)\implies f(5)=r(5)$