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.

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Question

$$\frac { 71647 } { 2128 }$$

Evaluate

$\frac{71647}{2128}\approx 33.668703008$

Steps For Long Division Method

Use the $1^{st}$ digit $7$ from dividend $71647$

$$\begin{array}{l}\phantom{2128)}\phantom{1}\\2128\overline{)71647}\\\end{array}$$

Since $7$ is less than $2128$, use the next digit $1$ from dividend $71647$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{2128)}0\phantom{2}\\2128\overline{)71647}\\\end{array}$$

Use the $2^{nd}$ digit $1$ from dividend $71647$

$$\begin{array}{l}\phantom{2128)}0\phantom{3}\\2128\overline{)71647}\\\end{array}$$

Since $71$ is less than $2128$, use the next digit $6$ from dividend $71647$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{2128)}00\phantom{4}\\2128\overline{)71647}\\\end{array}$$

Use the $3^{rd}$ digit $6$ from dividend $71647$

$$\begin{array}{l}\phantom{2128)}00\phantom{5}\\2128\overline{)71647}\\\end{array}$$

Since $716$ is less than $2128$, use the next digit $4$ from dividend $71647$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{2128)}000\phantom{6}\\2128\overline{)71647}\\\end{array}$$

Use the $4^{th}$ digit $4$ from dividend $71647$

$$\begin{array}{l}\phantom{2128)}000\phantom{7}\\2128\overline{)71647}\\\end{array}$$

Find closest multiple of $2128$ to $7164$. We see that $3 \times 2128 = 6384$ is the nearest. Now subtract $6384$ from $7164$ to get reminder $780$. Add $3$ to quotient.

$$\begin{array}{l}\phantom{2128)}0003\phantom{8}\\2128\overline{)71647}\\\phantom{2128)}\underline{\phantom{}6384\phantom{9}}\\\phantom{2128)9}780\\\end{array}$$

Use the $5^{th}$ digit $7$ from dividend $71647$

$$\begin{array}{l}\phantom{2128)}0003\phantom{9}\\2128\overline{)71647}\\\phantom{2128)}\underline{\phantom{}6384\phantom{9}}\\\phantom{2128)9}7807\\\end{array}$$

Find closest multiple of $2128$ to $7807$. We see that $3 \times 2128 = 6384$ is the nearest. Now subtract $6384$ from $7807$ to get reminder $1423$. Add $3$ to quotient.

$$\begin{array}{l}\phantom{2128)}00033\phantom{10}\\2128\overline{)71647}\\\phantom{2128)}\underline{\phantom{}6384\phantom{9}}\\\phantom{2128)9}7807\\\phantom{2128)}\underline{\phantom{9}6384\phantom{}}\\\phantom{2128)9}1423\\\end{array}$$

Since $1423$ is less than $2128$, stop the division. The reminder is $1423$. The topmost line $00033$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $33$.

$$\text{Quotient: }33$$ $$\text{Reminder: }1423$$

Show Solution

Factor

$\frac{71647}{2 ^ {4} \cdot 7 \cdot 19} = 33\frac{1423}{2128} = 33.6687030075188$

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Steps For Long Division Method

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