Precalculus Examples

$\frac{5 x^{2} - 17 x - 12}{x - 4}$

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 $a \cdot c = 5 \cdot - 12 = - 60$ and whose sum is $b = - 17$ .

Tap for more steps...

Step 1.1.1

Factor $- 17$ out of $- 17 x$ .

$\frac{5 x^{2} - 17 (x) - 12}{x - 4}$

Step 1.1.2

Rewrite $- 17$ as $3$ plus $- 20$

$\frac{5 x^{2} + (3 - 20) x - 12}{x - 4}$

Step 1.1.3

Apply the distributive property.

$\frac{5 x^{2} + 3 x - 20 x - 12}{x - 4}$

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.

$\frac{(5 x^{2} + 3 x) - 20 x - 12}{x - 4}$

Step 1.2.2

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

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

Step 1.3

Factor the polynomial by factoring out the greatest common factor, $5 x + 3$ .

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

Step 2

Cancel the common factor of $x - 4$ .

Tap for more steps...

Step 2.1

Cancel the common factor.

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

Step 2.2

Divide $5 x + 3$ by $1$ .

$5 x + 3$