Algebra Examples

$- 8 x^{2} - 15 x + 2$

Step 1

Factor $- 1$ out of $- 8 x^{2} - 15 x + 2$ .

Tap for more steps...

Step 1.1

Factor $- 1$ out of $- 8 x^{2}$ .

$- (8 x^{2}) - 15 x + 2$

Step 1.2

Factor $- 1$ out of $- 15 x$ .

$- (8 x^{2}) - (15 x) + 2$

Step 1.3

Rewrite $2$ as $- 1 (- 2)$ .

$- (8 x^{2}) - (15 x) - 1 (- 2)$

Step 1.4

Factor $- 1$ out of $- (8 x^{2}) - (15 x)$ .

$- (8 x^{2} + 15 x) - 1 (- 2)$

Step 1.5

Factor $- 1$ out of $- (8 x^{2} + 15 x) - 1 (- 2)$ .

$- (8 x^{2} + 15 x - 2)$

Step 2

Factor.

Tap for more steps...

Step 2.1

Factor by grouping.

Tap for more steps...

Step 2.1.1

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 $a \cdot c = 8 \cdot - 2 = - 16$ and whose sum is $b = 15$ .

Tap for more steps...

Step 2.1.1.1

Factor $15$ out of $15 x$ .

$- (8 x^{2} + 15 (x) - 2)$

Step 2.1.1.2

Rewrite $15$ as $- 1$ plus $16$

$- (8 x^{2} + (- 1 + 16) x - 2)$

Step 2.1.1.3

Apply the distributive property.

$- (8 x^{2} - 1 x + 16 x - 2)$

Step 2.1.2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 2.1.2.1

Group the first two terms and the last two terms.

$- ((8 x^{2} - 1 x) + 16 x - 2)$

Step 2.1.2.2

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

$- (x (8 x - 1) + 2 (8 x - 1))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $8 x - 1$ .

$- ((8 x - 1) (x + 2))$

Step 2.2

Remove unnecessary parentheses.

$- (8 x - 1) (x + 2)$