QuestionJuly 28, 2025

Write the quotient in simplest form. 2m+3longdiv (4m^3+2m^2-4m+3) A. 2m+m-1 B. 2m-m-1 C. 2m^2-2m+1 D. 2m^2+2m-1 Please select the best answer from the choices provided A B C D

Write the quotient in simplest form. 2m+3longdiv (4m^3+2m^2-4m+3) A. 2m+m-1 B. 2m-m-1 C. 2m^2-2m+1 D. 2m^2+2m-1 Please select the best answer from the choices provided A B C D
Write the quotient in simplest form. 2m+3longdiv (4m^3+2m^2-4m+3) A. 2m+m-1 B. 2m-m-1 C. 2m^2-2m+1 D. 2m^2+2m-1 Please select the best answer from the choices provided A B C D

Solution
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Answer

2m^2 - 2m + 1 (Option C) Explanation 1. Perform Polynomial Long Division Divide the first term of the dividend 4m^3 by the first term of the divisor 2m, which gives 2m^2. Multiply the entire divisor by 2m^2 and subtract from the original polynomial. 2. Continue Division Process The result is 2m^2 \cdot (2m + 3) = 4m^3 + 6m^2. Subtract this from 4m^3 + 2m^2 - 4m + 3 to get -4m^2 - 4m + 3. 3. Repeat for Next Term Divide -4m^2 by 2m to get -2m. Multiply the divisor by -2m and subtract. This results in -4m^2 - 6m. Subtracting gives 2m + 3. 4. Final Division Divide 2m by 2m to get 1. Multiply the divisor by 1 and subtract, resulting in a remainder of 0.

Explanation

1. Perform Polynomial Long Division<br /> Divide the first term of the dividend $4m^3$ by the first term of the divisor $2m$, which gives $2m^2$. Multiply the entire divisor by $2m^2$ and subtract from the original polynomial.<br />2. Continue Division Process<br /> The result is $2m^2 \cdot (2m + 3) = 4m^3 + 6m^2$. Subtract this from $4m^3 + 2m^2 - 4m + 3$ to get $-4m^2 - 4m + 3$.<br />3. Repeat for Next Term<br /> Divide $-4m^2$ by $2m$ to get $-2m$. Multiply the divisor by $-2m$ and subtract. This results in $-4m^2 - 6m$. Subtracting gives $2m + 3$.<br />4. Final Division<br /> Divide $2m$ by $2m$ to get $1$. Multiply the divisor by $1$ and subtract, resulting in a remainder of $0$.
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