How do you factor 3z^5 - 3z^2?

May 1, 2018

$3 {z}^{5} - 3 {z}^{2}$= $3 {z}^{2} \left({z}^{3} - 1\right)$

Explanation:

in this case you need to take out common factors from both terms. remember that factors should multiply together to give you your starting question so you can always use that as a check at the end.

if you can't immediately see the factors to take out then you can expand each of the terms first, look to see what is common to both of them, and then take the common ones out of each of term, leaving them outside a paranthesis, and inside the parenthesis you write whatever is left over.

lets expand first:

$3 {z}^{5} - 3 {z}^{2}$ becomes $3. z . z . z . z . z - 3. z . z$

well, there is a 3 in both terms , and there are two zs in both terms. so lets take those to the outside of the paranthesis

$3. z . z \left(1. z . z . z - 1\right)$ taking 3 from both terms leaves the 1 in both. and taking the z's leaves however many are left.... lets clean up the answer

$3 {z}^{2} \left(3 {z}^{3} - 1\right)$

and we're good. hope that helps