Thread: Factor a cubic without using CAS

How do you factor without a computer? (Obviously, I used a computer).

Originally Posted by MSUMathStdnt

How do you factor without a computer? (Obviously, I used a computer).

Are you aware of the Rational Root Theorem?

For convenience I'm going to divide the polynomial by 6:


Possible rational roots to this polynomial equation are:


That gives you 12 possible rational roots that you can check.

If you don't know that one, then you're probably stuck with Cardano's method. (Cardano's method is about 1/2 way down the page.)

-Dan

Originally Posted by MSUMathStdnt

How do you factor without a computer? (Obviously, I used a computer).

If we just start with , look for nice roots.

sort of pops out. So must be a factor.

Once we have one factor then by division we can reduce that to a quadratic which can factored.

I understand that it is not always possible to find a root that easily.