How to factorise $x^4 - 3x^3 + 2$, so as to compute the limit of a quotient? Question:

Find the limit: $$\lim_{x \to 1}\frac{x^4 - 3x^3 + 2}{x^3 -5x^2+3x+1}$$

The denominator can be simplified to: $$(x-1)(x^2+x)$$
However, I am unable to factor the numerator in a proper manner (so that $(x-1)$ will cancel out)
I know upon graphing that the limit is $5\over4$. What should I do here?
Note: To be done without the use of L'Hospital Rule

Here are the steps
$$\lim_{x \to 1}\frac{x^4 - 3x^3 + 2}{x^3 -5x^2+3x+1}$$
$$= \lim_{x \to 1}\frac{(x-1)(x^3- 2x^2-2x-2)}{(x-1)(x^2-4x-1)} $$
$$= \lim_{x \to 1}\frac{x^3- 2x^2-2x-2}{x^2-4x-1} $$
$$= \frac{1- 2-2-2}{1-4-1} = \frac{1- 6}{1-5}  = \frac{5}{4} $$
