Algebra Examples

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

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

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

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

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

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

Step 3.1.2

Factor $2 x$ out of $4 x$ .

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

Step 3.1.3

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

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $2$ out of $4$ .

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

Step 3.2.2.2

Cancel the common factor.

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

Step 3.2.2.3

Rewrite the expression.

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

Step 3.3

Move the negative in front of the fraction.

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

Step 4

Reorder terms.

$\frac{1}{2} x (x^{3} + 2) - \frac{5}{4}$