SOLUTION: I sort of know how to factor a perfect square but I can't figur out how to factor a cube. Factor x*3-125. Do I find the square root of a number?

Question 73618: I sort of know how to factor a perfect square but I can't figur out how to factor a cube. Factor x*3-125. Do I find the square root of a number?
Found 2 solutions by bucky, joyofmath:
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The easiest way to do this one is to make this an equation by setting it equal to zero to get:
.

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Then add 125 to both sides to get:
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.
Then take the cube root of both sides. Note that the cube root of 125 is 5 because 5*5*5 = 125.
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And the cube root of is just . So the solution is just:
.

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Subtract 5 from both sides to get:
.

.
This tells you that a factor is x-5. Divide this factor into and you
find that the quotient is
.
This does not factor further into real numbers. At this stopping point, the answer to
your factoring problem is that it factors into
.
If you are into complex numbers, you can use the same technique to factor
Set it equal to zero and apply the quadratic formula to get that the answers are:
.

.
These convert into factors of:
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and
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As a result this makes your three factors of equal:
.

.
This is tricky to understand so I hope it hasn't overwhelmed you. Give me a response to
indicate if you need further explanation of this factoring method.
Answer by joyofmath(189) (Show Source): You can put this solution on YOUR website!
Let's look at the general case, how to factor .
By the binomial theorem, .
So, .
Or, .
So, for the problem at hand we substitute a=x and b=5 and we get
.
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