Precalculus Examples

$x^{2} - 9$ and $x^{2} - 5 x + 6$

Step 1

Add $x^{2}$ and $x^{2}$ .

$2 x^{2} - 9 - 5 x + 6$

Step 2

Add $- 9$ and $6$ .

$2 x^{2} - 5 x - 3$

Step 3

Factor by grouping.

Tap for more steps...

Step 3.1

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 $a \cdot c = 2 \cdot - 3 = - 6$ and whose sum is $b = - 5$ .

Tap for more steps...

Step 3.1.1

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

$2 x^{2} - 5 (x) - 3$

Step 3.1.2

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

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

Step 3.1.3

Apply the distributive property.

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

Step 3.1.4

Multiply $x$ by $1$ .

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

Step 3.2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 3.2.1

Group the first two terms and the last two terms.

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

Step 3.2.2

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

$x (2 x + 1) - 3 (2 x + 1)$

Step 3.3

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

$(2 x + 1) (x - 3)$