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

$$\frac { 2500 } { 75 }$$

Evaluate

$\frac{100}{3}\approx 33.333333333$

Steps For Long Division Method

Use the $1^{st}$ digit $2$ from dividend $2500$

$$\begin{array}{l}\phantom{75)}\phantom{1}\\75\overline{)2500}\\\end{array}$$

Since $2$ is less than $75$, use the next digit $5$ from dividend $2500$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{75)}0\phantom{2}\\75\overline{)2500}\\\end{array}$$

Use the $2^{nd}$ digit $5$ from dividend $2500$

$$\begin{array}{l}\phantom{75)}0\phantom{3}\\75\overline{)2500}\\\end{array}$$

Since $25$ is less than $75$, use the next digit $0$ from dividend $2500$ and add $0$ to the quotient

$$\begin{array}{l}\phantom{75)}00\phantom{4}\\75\overline{)2500}\\\end{array}$$

Use the $3^{rd}$ digit $0$ from dividend $2500$

$$\begin{array}{l}\phantom{75)}00\phantom{5}\\75\overline{)2500}\\\end{array}$$

Find closest multiple of $75$ to $250$. We see that $3 \times 75 = 225$ is the nearest. Now subtract $225$ from $250$ to get reminder $25$. Add $3$ to quotient.

$$\begin{array}{l}\phantom{75)}003\phantom{6}\\75\overline{)2500}\\\phantom{75)}\underline{\phantom{}225\phantom{9}}\\\phantom{75)9}25\\\end{array}$$

Use the $4^{th}$ digit $0$ from dividend $2500$

$$\begin{array}{l}\phantom{75)}003\phantom{7}\\75\overline{)2500}\\\phantom{75)}\underline{\phantom{}225\phantom{9}}\\\phantom{75)9}250\\\end{array}$$

Find closest multiple of $75$ to $250$. We see that $3 \times 75 = 225$ is the nearest. Now subtract $225$ from $250$ to get reminder $25$. Add $3$ to quotient.

$$\begin{array}{l}\phantom{75)}0033\phantom{8}\\75\overline{)2500}\\\phantom{75)}\underline{\phantom{}225\phantom{9}}\\\phantom{75)9}250\\\phantom{75)}\underline{\phantom{9}225\phantom{}}\\\phantom{75)99}25\\\end{array}$$

Since $25$ is less than $75$, stop the division. The reminder is $25$. The topmost line $0033$ is the quotient. Remove all zeros at the start of the quotient to get the actual quotient $33$.

$$\text{Quotient: }33$$ $$\text{Reminder: }25$$

Show Solution

Factor

$\frac{2 ^ {2} \cdot 5 ^ {2}}{3} = 33\frac{1}{3} = 33.333333333333336$