6z^3-12z^2+18z

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Question

6z^3-12z^2+18z 

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solomonzelman · Answer

You want to find the roots?

campbell_st · Answer

I'll write it in expanded form 

$$3z \times z^2 - 3z \times 4z + 3z \times 6$$

solomonzelman · Answer

If so,

I would do the following:
1.  Factor (the entire polynomial) out of $\large\color{slate}{6z }$.
2.  Factor the remaining part, (the one multiplied times $\large\color{slate}{6z }$.

anonymous · Answer

I got z(6z^2-12z+18) but that's not right..

campbell_st · Answer

well there is also a number that is a common factor to all

campbell_st · Answer

6, -12 , 18   the common factor is ..?

anonymous · Answer

So when there's a number that is divisible by all of them you divide it? So you would divide by 6.

campbell_st · Answer

that's correct... so that is taken outside with z... so its

anonymous · Answer

6z(z^2-6+3)

campbell_st · Answer

that's correct

anonymous · Answer

also, why wouldn't you divide the z and the 6.?

campbell_st · Answer

not quite... 6z is correct but its 

6z x -2z = -12z^2

6z x 3 = 18z

so its

6z(z^2 -2z + 3)

campbell_st · Answer

well if you are asked to factor... you need all the factors..

anonymous · Answer

how did you get the two?

campbell_st · Answer

the middle term in the original question is -12z^2

so  6z x -2z = -12z^2

anonymous · Answer

oh yeah nevermine I messed up. 12/6 is 2. thanks.