Question

Evaluate: $(2m^3+m^2+m+9)÷(2m-1)$

Answer 1

To find:

$(2m^3+m^2+m+9)÷(2m-1)$

Step 1:

$\frac{2m^3}{2m}=m^2$ and $m^2\times (2m-1)=2m^3-m^2$

Lets write $2m^3-m^2$ under $(2m^3+m^2+m+9)$ and then subtract.

Step 2:

$\frac{2m^2}{2m}=m$ and $m\times (2m-1)=2m^3-m$

Lets write $2m^3-m$ under $2m^2+m$ and then subtract.

Step 3:

$\frac{2m}{2m}=1$ and $1\times (2m-1)=2m-1$

Lets write $2m-1$ under $2m+9$ and then subtract.

Hence, the remainder is $10$.

$m^2+m+12m-1)\overline{2m^3+m^2+m+9}2m^3-m^2(-)-+\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_2m^2+m+92m^2-m(-)-+\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_2m+92m-1(-)-+\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_10$

From the division,

Quotient $=m^2+m+1$ and Remainder $=10$.