Question

Find the zeros of the function.

f(x) = 3x3 - 12x2 - 15x

Answer 1

Please explain as well :)

Answer 2

first step is to make f(x) 0

so you have 3x^3 - 12x^2 - 15x = 0

right?

Answer 3

Ok

Answer 4

now. factor out x from 3x^3 - 12x^2 - 15x

Answer 5

Ok so x(3x^2 - 12x -15)= 0

Answer 6

Is that right?

Answer 7

right

Answer 8

now..factor out 3x^2 - 12x + 15

Answer 9

wait. typo. factor out 3x^2 - 12x - 15

Answer 10

Ok... I understand that you need to factor that out but to be honest with you I always have trouble factoring when there's a number in front of the first x... So I would know how to factor out x^2-12x-15 but I'm confused because there's a 3 there.

Answer 11

So how do I do this?

Answer 12

you can break down the middle term

-12x is also equal to -15x + 3x right?

so you have 3x^2 - 15x + 3x - 15

do you know how to factor that out?

Answer 13

or wait..here's a better idea

Answer 14

can you see that 3, -12 and -15 are all divisible by 3?

Answer 15

Yes

Answer 16

so you can factor 3 out first

Answer 17

Ok so 3(x^2 - 4x -5)

Answer 18

Now what?

Answer 19

now. you said you can factor out if there's no number beside x^2 so factor out x^2 - 4x - 5

Answer 20

Ok so 3(x+1)(x-5)

Answer 21

Ohhh

Answer 22

do you see what to do now?

Answer 23

So the zeros are 0, -1, and 5

Answer 24

Thanks so much! :)

Answer 25

right