Precalculus Examples

$(m x^{3} + 3 x^{2} + n x - 2) \div (x - 1)$

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

Rewrite the division as a fraction.

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

Step 3

Split the fraction $\frac{m x^{3} + 3 x^{2} + n x - 2}{x - 1}$ into two fractions.

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

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

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

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

Step 4.1.2

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

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

Step 4.1.3

Factor $x$ out of $n x$ .

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

Step 4.1.4

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

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

Step 4.1.5

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

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

Step 4.2

Move the negative in front of the fraction.

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

Step 5

Move $3 x$ .

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