Algebra Examples

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

Step 1

Factor by grouping.

Tap for more steps...

Step 1.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = - 3 \cdot 2 = - 6$ and whose sum is $b = - 5$ .

Tap for more steps...

Step 1.1.1

Factor $- 5$ out of $- 5 x$ .

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

Step 1.1.2

Rewrite $- 5$ as $1$ plus $- 6$

$\frac{- 3 x^{2} + (1 - 6) x + 2}{x^{3} + 2 x^{2}}$

Step 1.1.3

Apply the distributive property.

$\frac{- 3 x^{2} + 1 x - 6 x + 2}{x^{3} + 2 x^{2}}$

Step 1.1.4

Multiply $x$ by $1$ .

$\frac{- 3 x^{2} + x - 6 x + 2}{x^{3} + 2 x^{2}}$

Step 1.2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 1.2.1

Group the first two terms and the last two terms.

$\frac{(- 3 x^{2} + x) - 6 x + 2}{x^{3} + 2 x^{2}}$

Step 1.2.2

Factor out the greatest common factor (GCF) from each group.

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

Step 1.3

Factor the polynomial by factoring out the greatest common factor, $- 3 x + 1$ .

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

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Factor $x^{2}$ out of $x^{2} x + x^{2} \cdot 2$ .

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

Step 3

Cancel the common factor of $x + 2$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Factor $- 1$ out of $- 3 x$ .

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

Step 5

Rewrite $1$ as $- 1 (- 1)$ .

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

Step 6

Factor $- 1$ out of $- (3 x) - 1 (- 1)$ .

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

Step 7

Simplify the expression.

Tap for more steps...

Step 7.1

Rewrite $- (3 x - 1)$ as $- 1 (3 x - 1)$ .

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

Step 7.2

Move the negative in front of the fraction.

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