Divide (3x^5+x^4-4x^2)/x

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

Step 1

Factor $x^{2}$ out of $3 x^{5} + x^{4} - 4 x^{2}$ .

Factor $x^{2}$ out of $3 x^{5}$ .

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

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

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

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

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

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

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

Factor $x^{2}$ out of $x^{2} (3 x^{3} + x^{2}) + x^{2} \cdot - 4$ .

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

Step 2

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

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

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

Cancel the common factors.

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

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

Factor $x$ out of $x^{1}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $x (3 x^{3} + x^{2} - 4)$ by $1$ .

$x (3 x^{3} + x^{2} - 4)$

Step 3

Apply the distributive property.

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

Step 4

Simplify.

Rewrite using the commutative property of multiplication.

$3 x \cdot x^{3} + x \cdot x^{2} + x \cdot - 4$

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

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

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

$3 x \cdot x^{3} + x^{1} x^{2} + x \cdot - 4$

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

$3 x \cdot x^{3} + x^{1 + 2} + x \cdot - 4$

Add $1$ and $2$ .

$3 x \cdot x^{3} + x^{3} + x \cdot - 4$

Move $- 4$ to the left of $x$ .

$3 x \cdot x^{3} + x^{3} - 4 \cdot x$

Step 5

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

Move $x^{3}$ .

$3 (x^{3} x) + x^{3} - 4 \cdot x$

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

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

$3 (x^{3} x^{1}) + x^{3} - 4 \cdot x$

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

$3 x^{3 + 1} + x^{3} - 4 \cdot x$

Add $3$ and $1$ .

$3 x^{4} + x^{3} - 4 \cdot x$

$3 x^{4} + x^{3} - 4 x$

Divide (3x^5+x^4-4x^2)/x

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