Finite Math Examples

$15 z^{2} - 7 z^{3} - 2 z^{4}$

Step 1

Factor out the GCF of $z^{2}$ from $15 z^{2} - 7 z^{3} - 2 z^{4}$ .

Tap for more steps...

Step 1.1

Factor out the GCF of $z^{2}$ from each term in the polynomial.

Tap for more steps...

Step 1.1.1

Factor out the GCF of $z^{2}$ from the expression $15 z^{2}$ .

$z^{2} (15) - 7 z^{3} - 2 z^{4}$

Step 1.1.2

Factor out the GCF of $z^{2}$ from the expression $- 7 z^{3}$ .

$z^{2} (15) + z^{2} (- 7 z) - 2 z^{4}$

Step 1.1.3

Factor out the GCF of $z^{2}$ from the expression $- 2 z^{4}$ .

$z^{2} (15) + z^{2} (- 7 z) + z^{2} (- 2 z^{2})$

Step 1.2

Since all the terms share a common factor of $z^{2}$ , it can be factored out of each term.

$z^{2} (15 - 7 z - 2 z^{2})$

Step 2

Factor by grouping.

Tap for more steps...

Step 2.1

Reorder terms.

$z^{2} (- 2 z^{2} - 7 z + 15)$

Step 2.2

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 $a \cdot c = - 2 \cdot 15 = - 30$ and whose sum is $b = - 7$ .

Tap for more steps...

Step 2.2.1

Factor $- 7$ out of $- 7 z$ .

$z^{2} (- 2 z^{2} - 7 z + 15)$

Step 2.2.2

Rewrite $- 7$ as $3$ plus $- 10$

$z^{2} (- 2 z^{2} + (3 - 10) z + 15)$

Step 2.2.3

Apply the distributive property.

$z^{2} (- 2 z^{2} + 3 z - 10 z + 15)$

Step 2.3

Factor out the greatest common factor from each group.

Tap for more steps...

Step 2.3.1

Group the first two terms and the last two terms.

$z^{2} ((- 2 z^{2} + 3 z) - 10 z + 15)$

Step 2.3.2

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

$z^{2} (z (- 2 z + 3) + 5 (- 2 z + 3))$

Step 2.4

Factor the polynomial by factoring out the greatest common factor, $- 2 z + 3$ .

$z^{2} ((- 2 z + 3) (z + 5))$