When $x^{4}+k x^{2}-5$ is divided by $x^{2}+1$, the remainder is -6 . Find the value of $\mathbf{k}$.
a) -2
b) -1
c) 0
d) 1
e) 2

Answer

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Answer

$\boxed{k = 2}$

Steps

Step 1 ：Use polynomial long division to find the remainder when the given polynomial is divided by $x^2 + 1$

Step 2 ：Set the remainder equal to -6 and solve for k

Step 3 ：$-k - 4 = -6$

Step 4 ：$k = 2$

Step 5 ：$\boxed{k = 2}$