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

$$\frac { 8537 } { 21 }$$

Evaluate

$\frac{8537}{21}\approx 406.523809524$

Steps For Long Division Method

Use the $1^{st}$ digit $8$ from dividend $8537$

$$\begin{array}{l}\phantom{21)}\phantom{1}\\21\overline{)8537}\\\end{array}$$

Since $8$ is less than $21$, use the next digit $5$ from dividend $8537$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{21)}0\phantom{2}\\21\overline{)8537}\\\end{array}$$

Use the $2^{nd}$ digit $5$ from dividend $8537$

$$\begin{array}{l}\phantom{21)}0\phantom{3}\\21\overline{)8537}\\\end{array}$$

Find closest multiple of $21$ to $85$. We see that $4 \times 21 = 84$ is the nearest. Now subtract $84$ from $85$ to get reminder $1$. Add $4$ to quotient.

$$\begin{array}{l}\phantom{21)}04\phantom{4}\\21\overline{)8537}\\\phantom{21)}\underline{\phantom{}84\phantom{99}}\\\phantom{21)9}1\\\end{array}$$

Use the $3^{rd}$ digit $3$ from dividend $8537$

$$\begin{array}{l}\phantom{21)}04\phantom{5}\\21\overline{)8537}\\\phantom{21)}\underline{\phantom{}84\phantom{99}}\\\phantom{21)9}13\\\end{array}$$

Since $13$ is less than $21$, use the next digit $7$ from dividend $8537$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{21)}040\phantom{6}\\21\overline{)8537}\\\phantom{21)}\underline{\phantom{}84\phantom{99}}\\\phantom{21)9}13\\\end{array}$$

Use the $4^{th}$ digit $7$ from dividend $8537$

$$\begin{array}{l}\phantom{21)}040\phantom{7}\\21\overline{)8537}\\\phantom{21)}\underline{\phantom{}84\phantom{99}}\\\phantom{21)9}137\\\end{array}$$

Find closest multiple of $21$ to $137$. We see that $6 \times 21 = 126$ is the nearest. Now subtract $126$ from $137$ to get reminder $11$. Add $6$ to quotient.

$$\begin{array}{l}\phantom{21)}0406\phantom{8}\\21\overline{)8537}\\\phantom{21)}\underline{\phantom{}84\phantom{99}}\\\phantom{21)9}137\\\phantom{21)}\underline{\phantom{9}126\phantom{}}\\\phantom{21)99}11\\\end{array}$$

Since $11$ is less than $21$, stop the division. The reminder is $11$. The topmost line $0406$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $406$.

$$\text{Quotient: }406$$ $$\text{Reminder: }11$$

Show Solution

Factor

$\frac{8537}{3 \cdot 7} = 406\frac{11}{21} = 406.5238095238095$