Use long division to divide.
$$\left( x ^ { 4 } - x ^ { 2 } - 5 \right) \div \left( x ^ { 2 } + 4 x - 1 \right)$$
A) $x ^ { 2 } - 4 x + 4$
B) $x ^ { 2 } + 4 x - 4$
C) $x ^ { 2 } - 4 x + 16 + \frac { - 68 x + 11 } { x ^ { 2 } + 4 x - 1 }$
D) $x ^ { 2 } + 4 x - 4 + \frac { - 5 x - 1 } { x ^ { 2 } + 4 x - 1 }$
E) $x ^ { 2 } - 4 x + 4 - \frac { 4 } { x ^ { 2 } - 4 x + 4 }$

Question

Quizplus · Accepted Answer

To divide $(x^4 - x^2 - 5)$ by $(x^2 + 4x - 1)$, we start by dividing the leading term of the numerator, $x^4$, by the leading term of the denominator, $x^2$, to get $x^2$. Multiplying $x^2$ by the entire denominator $(x^2 + 4x - 1)$ and subtracting from the original polynomial gives a new polynomial. Repeating this process, we find that the quotient is $x^2 - 4x + 16$ with a remainder of $-68x + 11$. Therefore, the complete division is $x^2 - 4x + 16 + \frac{-68x + 11}{x^2 + 4x - 1}$.

Use Long Division to Divide (x4−x2−5)÷(x2+4x−1)\left( x ^ { 4 } - x ^ { 2 } - 5 \right) \div \left( x ^ { 2 } + 4 x - 1 \right)(x4−x2−5)÷(x2+4x−1)

Use Long Division to Divide $\left( x ^ { 4 } - x ^ { 2 } - 5 \right) \div \left( x ^ { 2 } + 4 x - 1 \right)$