Question

Given f(x) = x² + x + k, and the remainder when f(x) is divided by x-9 is 70,

then what is the value of k?

Answer 1

`k = -20`

Explanation:

According to the Remainder Theorem if you divide any polynomial,
`P(x)`, by
`D(x) = x -\blue{a}`, the remainder is
`P(\blue{a})`.

If you want
`f(x)` to have a remainder of
`70` when we divide it by
`x -\blue{9}`, we are essentially solving for
`f(\blue{9}) = 70`

`f(9) = 70 \\ (9)^2 +(9) +k = 70 \\ 81 +9 +k = 70 \\ k = 70 -81 -9 \\ k = -20`