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

$$\frac { 7834 } { 82 }$$

Evaluate

$\frac{3917}{41}\approx 95.536585366$

Steps For Long Division Method

Use the $1^{st}$ digit $7$ from dividend $7834$

$$\begin{array}{l}\phantom{82)}\phantom{1}\\82\overline{)7834}\\\end{array}$$

Since $7$ is less than $82$, use the next digit $8$ from dividend $7834$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{82)}0\phantom{2}\\82\overline{)7834}\\\end{array}$$

Use the $2^{nd}$ digit $8$ from dividend $7834$

$$\begin{array}{l}\phantom{82)}0\phantom{3}\\82\overline{)7834}\\\end{array}$$

Since $78$ is less than $82$, use the next digit $3$ from dividend $7834$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{82)}00\phantom{4}\\82\overline{)7834}\\\end{array}$$

Use the $3^{rd}$ digit $3$ from dividend $7834$

$$\begin{array}{l}\phantom{82)}00\phantom{5}\\82\overline{)7834}\\\end{array}$$

Find closest multiple of $82$ to $783$. We see that $9 \times 82 = 738$ is the nearest. Now subtract $738$ from $783$ to get reminder $45$. Add $9$ to quotient.

$$\begin{array}{l}\phantom{82)}009\phantom{6}\\82\overline{)7834}\\\phantom{82)}\underline{\phantom{}738\phantom{9}}\\\phantom{82)9}45\\\end{array}$$

Use the $4^{th}$ digit $4$ from dividend $7834$

$$\begin{array}{l}\phantom{82)}009\phantom{7}\\82\overline{)7834}\\\phantom{82)}\underline{\phantom{}738\phantom{9}}\\\phantom{82)9}454\\\end{array}$$

Find closest multiple of $82$ to $454$. We see that $5 \times 82 = 410$ is the nearest. Now subtract $410$ from $454$ to get reminder $44$. Add $5$ to quotient.

$$\begin{array}{l}\phantom{82)}0095\phantom{8}\\82\overline{)7834}\\\phantom{82)}\underline{\phantom{}738\phantom{9}}\\\phantom{82)9}454\\\phantom{82)}\underline{\phantom{9}410\phantom{}}\\\phantom{82)99}44\\\end{array}$$

Since $44$ is less than $82$, stop the division. The reminder is $44$. The topmost line $0095$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $95$.

$$\text{Quotient: }95$$ $$\text{Reminder: }44$$

Show Solution

Factor

$\frac{3917}{41} = 95\frac{22}{41} = 95.53658536585365$