Factors of x3 – 9x2 + 5x – 45 by grouping

Important:  Use the symbol "^" to denote exponentiation:

x3 – 9x2 + 5x – 45        NO
x^3 – 9x^2 + 5x – 45    YES

Look at the first 2 terms.  They can be rewritten as x^2(x-9).  Then look at the last 2 terms.  They can be rewritten as 5(x-9).  So, x-9 is the common factor here.   Thus, the original expression becomes:

(x^2-5)(x-9).

Note that x^2-5 can be factored, so that the final 3 factors are:

(x-sqrt(5)), (x+sqrt(5)), (x-9).