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

1 Answer
Dec 8, 2015

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.