Question

Find the remainder when f(x) = x3 − 14x2 51x − 22 is divided by x − 7.

Answer 1

The remainder is -8.

Answer 2

We can use at least two approaches in answering this question. But the easiest way is to use the
`<b>Remainder Theorem</b>`

According to the Remainder Theorem, if

`(x - a)`
is not a factor of

`f(x)`
then evaluating the function at

`x = a`
gives us the Remainder when

`f(x)`
is divided by

`(x - a)`
That is

`f(a) = R`


For the given question, we have


`f(x) = {x}^(3) - 14 {x}^(2) + 51x - 22`
When this function is divided by

`x - 7`
The remainder is given by

`f(7) = R`

`f(7) = {7}^(3) - 14( {7})^(2) + 51(7) - 22`

`f(7) = 343 - 14( 49) + 51(7) - 22`

`f(7) = 343 - 686+ 357 - 22`

`f(7) = - 8`

`<b>Hence the remainder is -8</b>`