# How do you factor #z^3-9x^2+27z-27#?

##### 2 Answers

Assuming that the

Notice that

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#### Explanation:

In the general case we have:

#(a+b)^3 = a^3+3a^2b+3ab^2+b^3#

In our case, we notice that

So try

#(z-3)^3 = z^3 + 3z^2(-3) + 3z(-3)^2 + (-3)^3#

#=z^3-9z^2+27z-27#

#### Explanation:

Let

We can set

If

∴ Possible values of

We can test a possible root by plugging in the value and seeing if

We find that

If

We can use synthetic division to divide

We get

So

We can factor the quadratic to get

So

∴