Use long division to divide.
$\left( x ^ { 4 } + 7 x ^ { 3 } + 10 x ^ { 2 } - x - 2 \right) \div ( x + 2 )$
A) $x ^ { 3 } + 5 x ^ { 2 } + 1$
B) $x ^ { 3 } - 5 x ^ { 2 } - 1$
C) $x ^ { 3 } + 5 x ^ { 2 } - 1$
D) $x ^ { 2 } + 5 x - 1$
E) $x ^ { 3 } - 5 x ^ { 2 } + 1$

Question

Use long division to divide.  
  $\left( x ^ { 4 } + 7 x ^ { 3 } + 10 x ^ { 2 } - x - 2 \right) \div ( x + 2 )$ 
A) $x ^ { 3 } + 5 x ^ { 2 } + 1$
B) $x ^ { 3 } - 5 x ^ { 2 } - 1$
C) $x ^ { 3 } + 5 x ^ { 2 } - 1$
D) $x ^ { 2 } + 5 x - 1$
E) $x ^ { 3 } - 5 x ^ { 2 } + 1$

Quizplus · Accepted Answer

Dividing $x^4 + 7x^3 + 10x^2 - x - 2$ by $x + 2$ using long division gives a quotient of $x^3 + 5x^2 - 10x + 19$ with a remainder of $36$. However, none of the options match this result exactly, indicating a mistake in my initial explanation. Correctly, the division process should yield $x^3 + 5x^2 - 10x + 20$ with a remainder of $38$, which still doesn't match any of the provided options. The correct approach simplifies to $x^3 + 5x^2 + 0x - 1$, which matches option C: $x^3 + 5x^2 - 1$. This discrepancy highlights the importance of carefully performing each step in polynomial long division.

Use Long Division to Divide (x4+7x3+10x2−x−2)÷(x+2)\left( x ^ { 4 } + 7 x ^ { 3 } + 10 x ^ { 2 } - x - 2 \right) \div ( x + 2 )(x4+7x3+10x2−x−2)÷(x+2)

Use Long Division to Divide $\left( x ^ { 4 } + 7 x ^ { 3 } + 10 x ^ { 2 } - x - 2 \right) \div ( x + 2 )$