Divide (12a^7-8a^5+a^4)/(4a^3)

$\frac{12 a^{7} - 8 a^{5} + a^{4}}{4 a^{3}}$

Factor $a^{4}$ out of $12 a^{7} - 8 a^{5} + a^{4}$ .

Factor $a^{4}$ out of $12 a^{7}$ .

$\frac{a^{4} (12 a^{3}) - 8 a^{5} + a^{4}}{4 a^{3}}$

Factor $a^{4}$ out of $- 8 a^{5}$ .

$\frac{a^{4} (12 a^{3}) + a^{4} (- 8 a) + a^{4}}{4 a^{3}}$

Multiply by $1$ .

$\frac{a^{4} (12 a^{3}) + a^{4} (- 8 a) + a^{4} \cdot 1}{4 a^{3}}$

Factor $a^{4}$ out of $a^{4} (12 a^{3}) + a^{4} (- 8 a)$ .

$\frac{a^{4} (12 a^{3} - 8 a) + a^{4} \cdot 1}{4 a^{3}}$

Factor $a^{4}$ out of $a^{4} (12 a^{3} - 8 a) + a^{4} \cdot 1$ .

$\frac{a^{4} (12 a^{3} - 8 a + 1)}{4 a^{3}}$

Cancel the common factor of $a^{4}$ and $a^{3}$ .

Factor $a^{3}$ out of $a^{4} (12 a^{3} - 8 a + 1)$ .

$\frac{a^{3} (a (12 a^{3} - 8 a + 1))}{4 a^{3}}$

Cancel the common factors.

Factor $a^{3}$ out of $4 a^{3}$ .

$\frac{a^{3} (a (12 a^{3} - 8 a + 1))}{a^{3} \cdot 4}$

Cancel the common factor.

$\frac{a^{3} (a (12 a^{3} - 8 a + 1))}{a^{3} \cdot 4}$

Rewrite the expression.

$\frac{a (12 a^{3} - 8 a + 1)}{4}$

Apply the distributive property.

$\frac{a (12 a^{3}) + a (- 8 a) + a \cdot 1}{4}$

Simplify.

Rewrite using the commutative property of multiplication.

$\frac{12 a \cdot a^{3} + a (- 8 a) + a \cdot 1}{4}$

Rewrite using the commutative property of multiplication.

$\frac{12 a \cdot a^{3} - 8 a \cdot a + a \cdot 1}{4}$

Multiply $a$ by $1$ .

$\frac{12 a \cdot a^{3} - 8 a \cdot a + a}{4}$

Simplify each term.

Multiply $a$ by $a^{3}$ by adding the exponents.

Move $a^{3}$ .

$\frac{12 (a^{3} a) - 8 a \cdot a + a}{4}$

Multiply $a^{3}$ by $a$ .

Raise $a$ to the power of $1$ .

$\frac{12 (a^{3} a^{1}) - 8 a \cdot a + a}{4}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{12 a^{3 + 1} - 8 a \cdot a + a}{4}$

Add $3$ and $1$ .

$\frac{12 a^{4} - 8 a \cdot a + a}{4}$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$\frac{12 a^{4} - 8 (a \cdot a) + a}{4}$

Multiply $a$ by $a$ .

$\frac{12 a^{4} - 8 a^{2} + a}{4}$

Split the fraction $\frac{12 a^{4} - 8 a^{2} + a}{4}$ into two fractions.

$\frac{12 a^{4} - 8 a^{2}}{4} + \frac{a}{4}$

Split the fraction $\frac{12 a^{4} - 8 a^{2}}{4}$ into two fractions.

$\frac{12 a^{4}}{4} + \frac{- 8 a^{2}}{4} + \frac{a}{4}$

Cancel the common factor of $12$ and $4$ .

Factor $4$ out of $12 a^{4}$ .

$\frac{4 (3 a^{4})}{4} + \frac{- 8 a^{2}}{4} + \frac{a}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$\frac{4 (3 a^{4})}{4 (1)} + \frac{- 8 a^{2}}{4} + \frac{a}{4}$

Cancel the common factor.

$\frac{4 (3 a^{4})}{4 \cdot 1} + \frac{- 8 a^{2}}{4} + \frac{a}{4}$

Rewrite the expression.

$\frac{3 a^{4}}{1} + \frac{- 8 a^{2}}{4} + \frac{a}{4}$

Divide $3 a^{4}$ by $1$ .

$3 a^{4} + \frac{- 8 a^{2}}{4} + \frac{a}{4}$

Cancel the common factor of $- 8$ and $4$ .

Factor $4$ out of $- 8 a^{2}$ .

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

Cancel the common factors.

Factor $4$ out of $4$ .

$3 a^{4} + \frac{4 (- 2 a^{2})}{4 (1)} + \frac{a}{4}$

Cancel the common factor.

$3 a^{4} + \frac{4 (- 2 a^{2})}{4 \cdot 1} + \frac{a}{4}$

Rewrite the expression.

$3 a^{4} + \frac{- 2 a^{2}}{1} + \frac{a}{4}$

Divide $- 2 a^{2}$ by $1$ .

$3 a^{4} - 2 a^{2} + \frac{a}{4}$

Divide (12a^7-8a^5+a^4)/(4a^3)

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