How do you factor #x^3 – 4x^2 +x + 6#?
2 Answers
Explanation:
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
Explanation:
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
Since