Question

Given f(x) = x³ + kx + 9, and the remainder when f(x) is divided by x − 2 is 7,

then what is the value of k?

Answer 1

k = -5

Explanation:

According to the Remainder Theorem, when we divide a polynomial f(x) by (x − c), the remainder is f(c).

Therefore, if we divide polynomial f(x) = x³ + kx + 9 by (x - 2) and the remainder is 7 then:

• f(2) = 7

To find the value of k, simply substitute x = 2 into the function, equate it to 7 and solve for k.

`\begin{aligned}f(2)=(2)^3 + k(2) + 9 &= 7\\8+2k+9&=7\\2k+17&=7\\2k&=-10\\k&=-5\end{aligned}`

Therefore, the value of k is -5.