Use long division to divide.
$\left( x ^ { 4 } + 4 x ^ { 2 } + 5 \right) \div \left( x ^ { 2 } + x + 4 \right)$
A) $x ^ { 2 } - x + 1 - \frac { 4 } { x ^ { 2 } - x + 1 }$
B) $x ^ { 2 } - x + 1 + \frac { 3 x + 1 } { x ^ { 2 } + x + 4 }$
C) $x ^ { 2 } - x + 1$
D) $x ^ { 2 } + x - 1$
E) $x ^ { 2 } + x - 1 + \frac { 3 x - 4 } { x ^ { 2 } + x + 4 }$

Question

Use long division to divide. 
$\left( x ^ { 4 } + 4 x ^ { 2 } + 5 \right) \div \left( x ^ { 2 } + x + 4 \right)$ 
A) $x ^ { 2 } - x + 1 - \frac { 4 } { x ^ { 2 } - x + 1 }$
B) $x ^ { 2 } - x + 1 + \frac { 3 x + 1 } { x ^ { 2 } + x + 4 }$
C) $x ^ { 2 } - x + 1$
D) $x ^ { 2 } + x - 1$
E) $x ^ { 2 } + x - 1 + \frac { 3 x - 4 } { x ^ { 2 } + x + 4 }$

Quizplus · Accepted Answer

When dividing $x^4 + 4x^2 + 5$ by $x^2 + x + 4$, the quotient is $x^2 - x + 1$ with a remainder of $3x + 1$. Therefore, the complete division expression is $x^2 - x + 1 + \frac{3x + 1}{x^2 + x + 4}$.

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

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