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

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) $x ^ { 2 } - 4 x + 4 - \frac { 4 } { x ^ { 2 } - 4 x + 4 }$

Quizplus · Accepted Answer

To divide $(x^4 - x^2 - 5)$ by $(x^2 + 4x - 1)$, we perform long division. The first term of the quotient is $x^2$ because $x^4$ divided by $x^2$ is $x^2$. Multiplying $x^2$ by the divisor $(x^2 + 4x - 1)$ gives $x^4 + 4x^3 - x^2$. Subtracting this from the original polynomial gives $-4x^3 - 5$. Repeating the process, the next term in the quotient is $-4x$, leading to a remainder of $-68x + 11$. Thus, the correct 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 $\left( x ^ { 4 } - x ^ { 2 } - 5 \right) \div \left( x ^ { 2 } + 4 x - 1 \right)$