Question

Alright, I don't want someone to tell me the answer, just want help to start it? :) 3z^2+12z/z^4

Answer 1

The problem is

\[\Large \frac{3z^2+12z}{z^4}\]

right?

Answer 2

Yes

Answer 3

what do 3z^2, 12z and z^4 all have in common (in terms of factors)?

Answer 4

z

Answer 5

so factor that out of the numerator 3z^2 + 12z to get ???

Answer 6

3(z^2+4) ?

Answer 7

factor out z not 3

Answer 8

i don't know then..

Answer 9

z^2 is the same as z*z

Answer 10

so 3z^2 = 3*z*z = z*3z

Answer 11

12z is z*12

Answer 12

3z^2 + 12z

z*3z + z*12

z(3z + 12) ... using distributive property

Answer 13

ok, so then what?

Answer 14

z^4 is the same as z*z^3

Answer 15

so

\[\Large \frac{3z^2+12z}{z^4}\]

turns into

\[\Large \frac{z(3z + 12)}{z*z^3}\]

Answer 16

what cancels?

Answer 17

z cancels out?

Answer 18

so its 3z+12/z^3 ?

Answer 19

correct,

\[\Large \frac{3z + 12}{z^3}\]

Answer 20

so when it comes to simplifying things like this, you factor as much as possible and look for any cancellations

Answer 21

great thank you so much!! :)

Answer 22

you're welcome