Question

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

A.93
B.57
C.43
D.107

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


`(f(t))/(t-5)=q(t)+(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)`