Basic Math Examples

45 v^{2} + 22 v - 3

$45 v^{2} + 22 v - 3$

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 = 45 \cdot - 3 = - 135

$a \cdot c = 45 \cdot - 3 = - 135$ and whose sum is

b = 22

$b = 22$ .

Tap for more steps...

Step 1.1

Factor

22

$22$ out of

22 v

$22 v$ .

45 v^{2} + 22 (v) - 3

$45 v^{2} + 22 (v) - 3$

Step 1.2

Rewrite

22

$22$ as

- 5

$- 5$ plus

27

$27$

45 v^{2} + (- 5 + 27) v - 3

$45 v^{2} + (- 5 + 27) v - 3$

Step 1.3

Apply the distributive property.

45 v^{2} - 5 v + 27 v - 3

$45 v^{2} - 5 v + 27 v - 3$

45 v^{2} - 5 v + 27 v - 3

$45 v^{2} - 5 v + 27 v - 3$

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.

(45 v^{2} - 5 v) + 27 v - 3

$(45 v^{2} - 5 v) + 27 v - 3$

Step 2.2

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

5 v (9 v - 1) + 3 (9 v - 1)

$5 v (9 v - 1) + 3 (9 v - 1)$

5 v (9 v - 1) + 3 (9 v - 1)

$5 v (9 v - 1) + 3 (9 v - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor,

9 v - 1

$9 v - 1$ .

(9 v - 1) (5 v + 3)

$(9 v - 1) (5 v + 3)$