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

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Answer 1 · 2016-08-07T17:36:33

#93#.

As per the Remainder Theorem , if a Polynomial #P(t)# is divided

by #(t-a)#, the Remainder is #P(a)#.

Hence, we have, the remainder #P(5)=3(5)^2+5(5)-7=93#.

Otherwise, let us observe that,

#P(t)=3t^2+5t-7=3t^2-15t+20t-100+93#

#=3t(t-5)+20(t-5)+93=(t-5)(3t+20)+93#, so the

remainder, after division of #P(t)# by #(t-5)# will be #93#, as before!

Enjoy Maths.!