Divide using long division: $\frac { x ^ { 3 } + x ^ { 2 } + 5 } { x ^ { 2 } + 3 x - 1 }$
A) $x - 2 + \frac { 7 x + 3 } { x ^ { 2 } + 3 x - 1 }$
B) $x - 2 + \frac { 5 x + 3 } { x ^ { 2 } + 3 x - 1 }$
C) $x + 4 + \frac { 11 x + 1 } { x ^ { 2 } + 3 x - 1 }$
D) $x - 2 + \frac { 12 x - 2 } { x ^ { 2 } + 3 x - 1 }$

Question

Quizplus · Accepted Answer

To divide $x^3 + x^2 + 5$ by $x^2 + 3x - 1$, we start by dividing $x^3$ by $x^2$ to get $x$. Multiplying $x$ by $x^2 + 3x - 1$ gives $x^3 + 3x^2 - x$. Subtracting this from the original polynomial, we get $-2x^2 + x + 5$. Next, we divide $-2x^2$ by $x^2$ to get $-2$, and multiply $-2$ by $x^2 + 3x - 1$ to get $-2x^2 - 6x + 2$. Subtracting this from $-2x^2 + x + 5$ gives $7x + 3$. Thus, the quotient is $x - 2$ with a remainder of $7x + 3$, making the complete division $x - 2 + \frac{7x + 3}{x^2 + 3x - 1}$.

Divide Using Long Division x3+x2+5x2+3x−1\frac { x ^ { 3 } + x ^ { 2 } + 5 } { x ^ { 2 } + 3 x - 1 }x2+3x−1x3+x2+5​

Divide Using Long Division $\frac { x ^ { 3 } + x ^ { 2 } + 5 } { x ^ { 2 } + 3 x - 1 }$