Question

When x^4 + k is divided by x + 2, the remainder is 3. The value of k is

Answer 1

Explanation:

If any polynomial function f(x) = ax^4 + bx^3 + cx^2 + dx + e is divided by (x + m), then the remainder obtained is f(-m).

So if polynomial x^4 + k is divided by x + 2 then remainder is,

$(-2)^4+k=16+k$

But the remainder is 3. So equation for k is,

$16+k=3$

Simplify the equation for k.

$\begin{gathered} 16+k=3 \\ k=3-16 \\ =-13 \end{gathered}$

So value of k is -13.

Answer: -13