Divide (4x^8-10x^6-5x^4)/(2x^3)

$\frac{4 x^{8} - 10 x^{6} - 5 x^{4}}{2 x^{3}}$

Step 1

Factor $x^{4}$ out of $4 x^{8} - 10 x^{6} - 5 x^{4}$ .

Factor $x^{4}$ out of $4 x^{8}$ .

$\frac{x^{4} (4 x^{4}) - 10 x^{6} - 5 x^{4}}{2 x^{3}}$

Factor $x^{4}$ out of $- 10 x^{6}$ .

$\frac{x^{4} (4 x^{4}) + x^{4} (- 10 x^{2}) - 5 x^{4}}{2 x^{3}}$

Factor $x^{4}$ out of $- 5 x^{4}$ .

$\frac{x^{4} (4 x^{4}) + x^{4} (- 10 x^{2}) + x^{4} \cdot - 5}{2 x^{3}}$

Factor $x^{4}$ out of $x^{4} (4 x^{4}) + x^{4} (- 10 x^{2})$ .

$\frac{x^{4} (4 x^{4} - 10 x^{2}) + x^{4} \cdot - 5}{2 x^{3}}$

Factor $x^{4}$ out of $x^{4} (4 x^{4} - 10 x^{2}) + x^{4} \cdot - 5$ .

$\frac{x^{4} (4 x^{4} - 10 x^{2} - 5)}{2 x^{3}}$

Step 2

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

Factor $x^{3}$ out of $x^{4} (4 x^{4} - 10 x^{2} - 5)$ .

$\frac{x^{3} (x (4 x^{4} - 10 x^{2} - 5))}{2 x^{3}}$

Cancel the common factors.

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

$\frac{x^{3} (x (4 x^{4} - 10 x^{2} - 5))}{x^{3} \cdot 2}$

Cancel the common factor.

$\frac{x^{3} (x (4 x^{4} - 10 x^{2} - 5))}{x^{3} \cdot 2}$

Rewrite the expression.

$\frac{x (4 x^{4} - 10 x^{2} - 5)}{2}$

Step 3

Apply the distributive property.

$\frac{x (4 x^{4}) + x (- 10 x^{2}) + x \cdot - 5}{2}$

Step 4

Simplify.

Rewrite using the commutative property of multiplication.

$\frac{4 x \cdot x^{4} + x (- 10 x^{2}) + x \cdot - 5}{2}$

Rewrite using the commutative property of multiplication.

$\frac{4 x \cdot x^{4} - 10 x \cdot x^{2} + x \cdot - 5}{2}$

Move $- 5$ to the left of $x$ .

$\frac{4 x \cdot x^{4} - 10 x \cdot x^{2} - 5 \cdot x}{2}$

Step 5

Simplify each term.

Multiply $x$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$\frac{4 (x^{4} x) - 10 x \cdot x^{2} - 5 \cdot x}{2}$

Multiply $x^{4}$ by $x$ .

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

$\frac{4 (x^{4} x^{1}) - 10 x \cdot x^{2} - 5 \cdot x}{2}$

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

$\frac{4 x^{4 + 1} - 10 x \cdot x^{2} - 5 \cdot x}{2}$

Add $4$ and $1$ .

$\frac{4 x^{5} - 10 x \cdot x^{2} - 5 \cdot x}{2}$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$\frac{4 x^{5} - 10 (x^{2} x) - 5 \cdot x}{2}$

Multiply $x^{2}$ by $x$ .

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

$\frac{4 x^{5} - 10 (x^{2} x^{1}) - 5 \cdot x}{2}$

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

$\frac{4 x^{5} - 10 x^{2 + 1} - 5 \cdot x}{2}$

Add $2$ and $1$ .

$\frac{4 x^{5} - 10 x^{3} - 5 \cdot x}{2}$

$\frac{4 x^{5} - 10 x^{3} - 5 x}{2}$

Step 6

Split the fraction $\frac{4 x^{5} - 10 x^{3} - 5 x}{2}$ into two fractions.

$\frac{4 x^{5} - 10 x^{3}}{2} + \frac{- 5 x}{2}$

Step 7

Split the fraction $\frac{4 x^{5} - 10 x^{3}}{2}$ into two fractions.

$\frac{4 x^{5}}{2} + \frac{- 10 x^{3}}{2} + \frac{- 5 x}{2}$

Step 8

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

Factor $2$ out of $4 x^{5}$ .

$\frac{2 (2 x^{5})}{2} + \frac{- 10 x^{3}}{2} + \frac{- 5 x}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (2 x^{5})}{2 (1)} + \frac{- 10 x^{3}}{2} + \frac{- 5 x}{2}$

Cancel the common factor.

$\frac{2 (2 x^{5})}{2 \cdot 1} + \frac{- 10 x^{3}}{2} + \frac{- 5 x}{2}$

Rewrite the expression.

$\frac{2 x^{5}}{1} + \frac{- 10 x^{3}}{2} + \frac{- 5 x}{2}$

Divide $2 x^{5}$ by $1$ .

$2 x^{5} + \frac{- 10 x^{3}}{2} + \frac{- 5 x}{2}$

Step 9

Cancel the common factor of $- 10$ and $2$ .

Factor $2$ out of $- 10 x^{3}$ .

$2 x^{5} + \frac{2 (- 5 x^{3})}{2} + \frac{- 5 x}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$2 x^{5} + \frac{2 (- 5 x^{3})}{2 (1)} + \frac{- 5 x}{2}$

Cancel the common factor.

$2 x^{5} + \frac{2 (- 5 x^{3})}{2 \cdot 1} + \frac{- 5 x}{2}$

Rewrite the expression.

$2 x^{5} + \frac{- 5 x^{3}}{1} + \frac{- 5 x}{2}$

Divide $- 5 x^{3}$ by $1$ .

$2 x^{5} - 5 x^{3} + \frac{- 5 x}{2}$

Step 10

Move the negative in front of the fraction.

$2 x^{5} - 5 x^{3} - \frac{5 x}{2}$

Divide (4x^8-10x^6-5x^4)/(2x^3)

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