How do you factor #x^3 – 4x^2 +x + 6#?
It is usually really, really hard to factorize a cubic function. However, for this polynomial, we can factor by grouping. We try values for splitting the term
For example, we split it into
The equation becomes this:
Factoring the common factor out, we get
The fully factored form is then
Provided the expression has rational roots, we can use the rational root theorem.
For the expression
according to the rational root theorem, possible rational roots are:
With the use of a spreadsheet these values can be easily checked (it can also be done with a calculator or even manually with a bit more effort).
From this, we see that
This implies that