# 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