# How do you use the remainder theorem to determine the remainder when 3t^ 2 + 5t – 7 is divided by t – 5?

Aug 7, 2016

$93$.

#### Explanation:

As per the Remainder Theorem , if a Polynomial $P \left(t\right)$ is divided

by $\left(t - a\right)$, the Remainder is $P \left(a\right)$.

Hence, we have, the remainder $P \left(5\right) = 3 {\left(5\right)}^{2} + 5 \left(5\right) - 7 = 93$.

Otherwise, let us observe that,

$P \left(t\right) = 3 {t}^{2} + 5 t - 7 = 3 {t}^{2} - 15 t + 20 t - 100 + 93$

$= 3 t \left(t - 5\right) + 20 \left(t - 5\right) + 93 = \left(t - 5\right) \left(3 t + 20\right) + 93$, so the

remainder, after division of $P \left(t\right)$ by $\left(t - 5\right)$ will be $93$, as before!

Enjoy Maths.!