Finite Math Examples

$12 w^{3} - 39 w^{2} + 9 w$

Step 1

Factor out the GCF of $3 w$ from $12 w^{3} - 39 w^{2} + 9 w$ .

Tap for more steps...

Step 1.1

Factor out the GCF of $3 w$ from each term in the polynomial.

Tap for more steps...

Step 1.1.1

Factor out the GCF of $3 w$ from the expression $12 w^{3}$ .

$3 w (4 w^{2}) - 39 w^{2} + 9 w$

Step 1.1.2

Factor out the GCF of $3 w$ from the expression $- 39 w^{2}$ .

$3 w (4 w^{2}) + 3 w (- 13 w) + 9 w$

Step 1.1.3

Factor out the GCF of $3 w$ from the expression $9 w$ .

$3 w (4 w^{2}) + 3 w (- 13 w) + 3 w (3)$

Step 1.2

Since all the terms share a common factor of $3 w$ , it can be factored out of each term.

$3 w (4 w^{2} - 13 w + 3)$

Step 2

Factor by grouping.

Tap for more steps...

Step 2.1

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 $a \cdot c = 4 \cdot 3 = 12$ and whose sum is $b = - 13$ .

Tap for more steps...

Step 2.1.1

Factor $- 13$ out of $- 13 w$ .

$3 w (4 w^{2} - 13 w + 3)$

Step 2.1.2

Rewrite $- 13$ as $- 1$ plus $- 12$

$3 w (4 w^{2} + (- 1 - 12) w + 3)$

Step 2.1.3

Apply the distributive property.

$3 w (4 w^{2} - 1 w - 12 w + 3)$

Step 2.2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 2.2.1

Group the first two terms and the last two terms.

$3 w ((4 w^{2} - 1 w) - 12 w + 3)$

Step 2.2.2

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

$3 w (w (4 w - 1) - 3 (4 w - 1))$

Step 2.3

Factor the polynomial by factoring out the greatest common factor, $4 w - 1$ .

$3 w ((4 w - 1) (w - 3))$