Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x2"   was replaced by   "x^2".  1 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  (((x3) -  2x2) -  9x) +  18

Step  2  :

Checking for a perfect cube :

 2.1    x³-2x²-9x+18  is not a perfect cube

Trying to factor by pulling out :

 2.2      Factoring:  x³-2x²-9x+18 

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -9x+18 
Group 2:  x³-2x² 

Pull out from each group separately :

Group 1:   (x-2) • (-9)
Group 2:   (x-2) • (x²)
               -------------------
Add up the two groups :
               (x-2)  •  (x²-9) 
Which is the desired factorization

Trying to factor as a Difference of Squares :

 2.3      Factoring:  x²-9 

Theory : A difference of two perfect squares,  A² - B²  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A² - AB + BA - B² =
         A² - AB + AB - B² =
         A² - B²

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 9 is the square of 3
Check :  x²  is the square of  x¹ 

Factorization is :       (x + 3)  •  (x - 3) 

Final result :

  (x + 3) • (x - 3) • (x - 2)