Find the quotient and remainder for the division problem. $\left( 5 x ^ { 3 } + 18 x ^ { 2 } - 3 x - 1 \right) \div \left( x ^ { 2 } + 4 x \right)$
A) Q: $5 x - 2$
R: $5 x + 1$
B) Q: $5 x + 2$
R: $5 x - 1$
C) Q: $5 x - 2$
R: 0
D) Q: $5 x - 2$
R: $5 x - 1$
E) Q: $5 x + 2$
R: 0

Question

Quizplus · Accepted Answer

To divide $(5x^3 + 18x^2 - 3x - 1)$ by $(x^2 + 4x)$, we first divide $5x^3$ by $x^2$ to get $5x$. Multiplying $5x$ by $x^2 + 4x$ gives $5x^3 + 20x^2$. Subtracting this from the original polynomial, we get $-2x^2 - 3x - 1$. Then, we divide $-2x^2$ by $x^2$ to get $-2$, and multiplying $-2$ by $x^2 + 4x$ gives $-2x^2 - 8x$. Subtracting this from $-2x^2 - 3x - 1$ gives $5x - 1$, which is the remainder. So, the quotient is $5x - 2$ and the remainder is $5x - 1$.

Find the Quotient and Remainder for the Division Problem (5x3+18x2−3x−1)÷(x2+4x)\left( 5 x ^ { 3 } + 18 x ^ { 2 } - 3 x - 1 \right) \div \left( x ^ { 2 } + 4 x \right)(5x3+18x2−3x−1)÷(x2+4x)

Find the Quotient and Remainder for the Division Problem $\left( 5 x ^ { 3 } + 18 x ^ { 2 } - 3 x - 1 \right) \div \left( x ^ { 2 } + 4 x \right)$