Basic Math Examples

6 y^{2} + 13 y - 28

$6 y^{2} + 13 y - 28$

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 - 28 = - 168

$a \cdot c = 6 \cdot - 28 = - 168$ and whose sum is

b = 13

$b = 13$ .

Tap for more steps...

Step 1.1

Factor

13

$13$ out of

13 y

$13 y$ .

6 y^{2} + 13 (y) - 28

$6 y^{2} + 13 (y) - 28$

Step 1.2

Rewrite

13

$13$ as

- 8

$- 8$ plus

21

$21$

6 y^{2} + (- 8 + 21) y - 28

$6 y^{2} + (- 8 + 21) y - 28$

Step 1.3

Apply the distributive property.

6 y^{2} - 8 y + 21 y - 28

$6 y^{2} - 8 y + 21 y - 28$

6 y^{2} - 8 y + 21 y - 28

$6 y^{2} - 8 y + 21 y - 28$

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 y^{2} - 8 y) + 21 y - 28

$(6 y^{2} - 8 y) + 21 y - 28$

Step 2.2

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

2 y (3 y - 4) + 7 (3 y - 4)

$2 y (3 y - 4) + 7 (3 y - 4)$

2 y (3 y - 4) + 7 (3 y - 4)

$2 y (3 y - 4) + 7 (3 y - 4)$

Step 3

Factor the polynomial by factoring out the greatest common factor,

3 y - 4

$3 y - 4$ .

(3 y - 4) (2 y + 7)

$(3 y - 4) (2 y + 7)$