Algebra Examples

$(4 x^{4} + 2 x^{3} + 2 x^{2}) \div (4 x^{2})$

Step 1

Rewrite the division as a fraction.

$\frac{4 x^{4} + 2 x^{3} + 2 x^{2}}{4 x^{2}}$

Step 2

Factor $2 x^{2}$ out of $4 x^{4} + 2 x^{3} + 2 x^{2}$ .

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Step 2.1

Factor $2 x^{2}$ out of $4 x^{4}$ .

$\frac{2 x^{2} (2 x^{2}) + 2 x^{3} + 2 x^{2}}{4 x^{2}}$

Step 2.2

Factor $2 x^{2}$ out of $2 x^{3}$ .

$\frac{2 x^{2} (2 x^{2}) + 2 x^{2} (x) + 2 x^{2}}{4 x^{2}}$

Step 2.3

Factor $2 x^{2}$ out of $2 x^{2}$ .

$\frac{2 x^{2} (2 x^{2}) + 2 x^{2} (x) + 2 x^{2} (1)}{4 x^{2}}$

Step 2.4

Factor $2 x^{2}$ out of $2 x^{2} (2 x^{2}) + 2 x^{2} (x)$ .

$\frac{2 x^{2} (2 x^{2} + x) + 2 x^{2} (1)}{4 x^{2}}$

Step 2.5

Factor $2 x^{2}$ out of $2 x^{2} (2 x^{2} + x) + 2 x^{2} (1)$ .

$\frac{2 x^{2} (2 x^{2} + x + 1)}{4 x^{2}}$

Step 3

Cancel the common factor of $2$ and $4$ .

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Step 3.1

Factor $2$ out of $2 x^{2} (2 x^{2} + x + 1)$ .

$\frac{2 (x^{2} (2 x^{2} + x + 1))}{4 x^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $4 x^{2}$ .

$\frac{2 (x^{2} (2 x^{2} + x + 1))}{2 (2 x^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (x^{2} (2 x^{2} + x + 1))}{2 (2 x^{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{x^{2} (2 x^{2} + x + 1)}{2 x^{2}}$

Step 4

Cancel the common factor of $x^{2}$ .

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Step 4.1

Cancel the common factor.

$\frac{x^{2} (2 x^{2} + x + 1)}{2 x^{2}}$

Step 4.2

Rewrite the expression.

$\frac{2 x^{2} + x + 1}{2}$

Step 5

Split the fraction $\frac{2 x^{2} + x + 1}{2}$ into two fractions.

$\frac{2 x^{2} + x}{2} + \frac{1}{2}$

Step 6

Split the fraction $\frac{2 x^{2} + x}{2}$ into two fractions.

$\frac{2 x^{2}}{2} + \frac{x}{2} + \frac{1}{2}$

Step 7

Cancel the common factor of $2$ .

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Step 7.1

Cancel the common factor.

$\frac{2 x^{2}}{2} + \frac{x}{2} + \frac{1}{2}$

Step 7.2

Divide $x^{2}$ by $1$ .

$x^{2} + \frac{x}{2} + \frac{1}{2}$