Question

How do you use the remainder theorem to find the remainder for the division `(3t^3-10t^2+t-5)div(t-4)`?

Answer 1

The remainder is 31.

Explanation:

Remainder Theorem :
When we divide a polynomial `f(x)` by `(x−c)` the remainder is `f(c)`
So to find the remainder after dividing by `(x-c)` we don't need to do any division: Just calculate `f(c).`

In this case,
`f(4) = 3(4)^3 - 10(4)^2 + 4 - 5`
`f(4) = 31`

Answer 2

The remainder is 31.

Explanation:

Note that the dividend is equal to the divisor times the quotient plus the remainder.

Let Q equal the quotient and R the remainder.

`3t^3-10t^2+t-5=Q(t-4)+R`

Notice that when `t=4`, the divisor `t-4` becomes zero, meaning that anything multiplied to it will still result in zero.

Let's try `t=4`

`=>3(4)^3-10(4)^2+(4)-5=Q(4-4)+R`

`=>192-160+4-5=R`

`=>31=R`

That is the answer!

Answer 3

`31`

Explanation:

`"the remainder when "f(x)" is divided by "(x-a)" is "f(a)`

`3(4)^3-10(4)^2+4-5=31larrcolor(blue)"remainder"`