How to solve ( a ) 310752/96

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve ( a ) 310752/96 | Equatix

Use the $1^{st}$ digit $3$ from dividend $310752$

$$\begin{array}{l}\phantom{96)}\phantom{1}\\96\overline{)310752}\\\end{array}$$

Since $3$ is less than $96$, use the next digit $1$ from dividend $310752$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{96)}0\phantom{2}\\96\overline{)310752}\\\end{array}$$

Use the $2^{nd}$ digit $1$ from dividend $310752$

$$\begin{array}{l}\phantom{96)}0\phantom{3}\\96\overline{)310752}\\\end{array}$$

Since $31$ is less than $96$, use the next digit $0$ from dividend $310752$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{96)}00\phantom{4}\\96\overline{)310752}\\\end{array}$$

Use the $3^{rd}$ digit $0$ from dividend $310752$

$$\begin{array}{l}\phantom{96)}00\phantom{5}\\96\overline{)310752}\\\end{array}$$

Find closest multiple of $96$ to $310$. We see that $3 \times 96 = 288$ is the nearest. Now subtract $288$ from $310$ to get reminder $22$. Add $3$ to quotient.

$$\begin{array}{l}\phantom{96)}003\phantom{6}\\96\overline{)310752}\\\phantom{96)}\underline{\phantom{}288\phantom{999}}\\\phantom{96)9}22\\\end{array}$$

Use the $4^{th}$ digit $7$ from dividend $310752$

$$\begin{array}{l}\phantom{96)}003\phantom{7}\\96\overline{)310752}\\\phantom{96)}\underline{\phantom{}288\phantom{999}}\\\phantom{96)9}227\\\end{array}$$

Find closest multiple of $96$ to $227$. We see that $2 \times 96 = 192$ is the nearest. Now subtract $192$ from $227$ to get reminder $35$. Add $2$ to quotient.

$$\begin{array}{l}\phantom{96)}0032\phantom{8}\\96\overline{)310752}\\\phantom{96)}\underline{\phantom{}288\phantom{999}}\\\phantom{96)9}227\\\phantom{96)}\underline{\phantom{9}192\phantom{99}}\\\phantom{96)99}35\\\end{array}$$

Use the $5^{th}$ digit $5$ from dividend $310752$

$$\begin{array}{l}\phantom{96)}0032\phantom{9}\\96\overline{)310752}\\\phantom{96)}\underline{\phantom{}288\phantom{999}}\\\phantom{96)9}227\\\phantom{96)}\underline{\phantom{9}192\phantom{99}}\\\phantom{96)99}355\\\end{array}$$

Find closest multiple of $96$ to $355$. We see that $3 \times 96 = 288$ is the nearest. Now subtract $288$ from $355$ to get reminder $67$. Add $3$ to quotient.

$$\begin{array}{l}\phantom{96)}00323\phantom{10}\\96\overline{)310752}\\\phantom{96)}\underline{\phantom{}288\phantom{999}}\\\phantom{96)9}227\\\phantom{96)}\underline{\phantom{9}192\phantom{99}}\\\phantom{96)99}355\\\phantom{96)}\underline{\phantom{99}288\phantom{9}}\\\phantom{96)999}67\\\end{array}$$

Use the $6^{th}$ digit $2$ from dividend $310752$

$$\begin{array}{l}\phantom{96)}00323\phantom{11}\\96\overline{)310752}\\\phantom{96)}\underline{\phantom{}288\phantom{999}}\\\phantom{96)9}227\\\phantom{96)}\underline{\phantom{9}192\phantom{99}}\\\phantom{96)99}355\\\phantom{96)}\underline{\phantom{99}288\phantom{9}}\\\phantom{96)999}672\\\end{array}$$

Find closest multiple of $96$ to $672$. We see that $7 \times 96 = 672$ is the nearest. Now subtract $672$ from $672$ to get reminder $0$. Add $7$ to quotient.

$$\begin{array}{l}\phantom{96)}003237\phantom{12}\\96\overline{)310752}\\\phantom{96)}\underline{\phantom{}288\phantom{999}}\\\phantom{96)9}227\\\phantom{96)}\underline{\phantom{9}192\phantom{99}}\\\phantom{96)99}355\\\phantom{96)}\underline{\phantom{99}288\phantom{9}}\\\phantom{96)999}672\\\phantom{96)}\underline{\phantom{999}672\phantom{}}\\\phantom{96)999999}0\\\end{array}$$

Since $0$ is less than $96$, stop the division. The reminder is $0$. The topmost line $003237$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $3237$.

$$\text{Quotient: }3237$$ $$\text{Reminder: }0$$

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