Algebra Examples

6 x^{2} + 13 x - 63

$6 x^{2} + 13 x - 63$

Step 1

For a polynomial of the form

a x^{2} + b x + c

$a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is

a \cdot c = 6 \cdot - 63 = - 378

$a \cdot c = 6 \cdot - 63 = - 378$ and whose sum is

b = 13

$b = 13$ .

Tap for more steps...

Step 1.1

Factor

13

$13$ out of

13 x

$13 x$ .

6 x^{2} + 13 (x) - 63

$6 x^{2} + 13 (x) - 63$

Step 1.2

Rewrite

13

$13$ as

- 14

$- 14$ plus

27

$27$

6 x^{2} + (- 14 + 27) x - 63

$6 x^{2} + (- 14 + 27) x - 63$

Step 1.3

Apply the distributive property.

6 x^{2} - 14 x + 27 x - 63

$6 x^{2} - 14 x + 27 x - 63$

6 x^{2} - 14 x + 27 x - 63

$6 x^{2} - 14 x + 27 x - 63$

Step 2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 2.1

Group the first two terms and the last two terms.

(6 x^{2} - 14 x) + 27 x - 63

$(6 x^{2} - 14 x) + 27 x - 63$

Step 2.2

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

2 x (3 x - 7) + 9 (3 x - 7)

$2 x (3 x - 7) + 9 (3 x - 7)$

2 x (3 x - 7) + 9 (3 x - 7)

$2 x (3 x - 7) + 9 (3 x - 7)$

Step 3

Factor the polynomial by factoring out the greatest common factor,

3 x - 7

$3 x - 7$ .

(3 x - 7) (2 x + 9)

$(3 x - 7) (2 x + 9)$