Question

How do you factor #y=x^3 - 3x^2 + 4x -12 #?

Answer 1

You can use the grouping method to factor `y = x^3 - 3x^2 + 4x - 12` to get `(x^2 + 4)(x-3)`.

Explanation:

We can look at this equation in two parts, indicated by the parentheses:

`y = (x^3 - 3x^2) + (4x - 12)`

There, we just grouped the terms! (:
Now, do you notice anything about the groups?
You'll find that we can factor out an `x^2` from the first group and we can factor out a `4` from the second:

`y = x^2(x - 3) + 4(x-3)`

Hey look at that--what do you notice about our "leftover" terms? They're both `(x - 3)`. We can merge these together into one common `(x - 3)` term. And then we're going to do something that might be new for you; we're going to take the two terms that we just factored out (`x^2` and `4`), and add them to get one term to multiply the "leftovers" with:

`y = (x^2 + 4)(x - 3)`

And there you have it--factored form!
As a side note, if you wanted to solve this equation, all you would need to do from here is set the equation equal to zero ("plug in" 0 for `y`) and solve for `x` to get `x = +2i, -2i, and 3`.