Find the quotient and remainder for the division problem. $\left( 2 y ^ { 3 } - 3 y ^ { 2 } - 5 y - 2 \right) \div \left( y ^ { 2 } - y \right)$
A) $Q : 2 y - 1$
$$\mathrm { R } : - 3 y - 1$$
B) Q: $2 y - 1$
R: 0
C) $Q : - 6 y - 2$
$\mathrm { R } : 2 y - 1$
D) $\begin{array} { l }
\mathrm { Q } : 2 y - 1 \
\mathrm { R } : - 6 y - 2
\end{array}$
E) $Q : - 6 y - 2$
R: 0

Question

Find the quotient and remainder for the division problem. $\left( 2 y ^ { 3 } - 3 y ^ { 2 } - 5 y - 2 \right) \div \left( y ^ { 2 } - y \right)$
A) $Q : 2 y - 1$
$$\mathrm { R } : - 3 y - 1$$
B) Q: $2 y - 1$
R: 0
C) $Q : - 6 y - 2$
$\mathrm { R } : 2 y - 1$
D) $\begin{array} { l } 
\mathrm { Q } : 2 y - 1 \
\mathrm { R } : - 6 y - 2
\end{array}$
E) $Q : - 6 y - 2$
R: 0

Quizplus · Accepted Answer

We can use polynomial long division or synthetic division to solve this problem. Using polynomial long division, we get:

2y - 1
y^2 - y | 2y^3 - 3y^2 - 5y - 2
            2y^3 - 2y^2   
                   -y^2 - 5y
                   -y^2 + y
                         -6y - 2

Therefore, the quotient is 2y - 1 and the remainder is -6y - 2. Choice D matches this result, so it is the correct answer.

Find the Quotient and Remainder for the Division Problem (2y3−3y2−5y−2)÷(y2−y)\left( 2 y ^ { 3 } - 3 y ^ { 2 } - 5 y - 2 \right) \div \left( y ^ { 2 } - y \right)(2y3−3y2−5y−2)÷(y2−y)

Find the Quotient and Remainder for the Division Problem $\left( 2 y ^ { 3 } - 3 y ^ { 2 } - 5 y - 2 \right) \div \left( y ^ { 2 } - y \right)$