Solution - Polynomial long division

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "m3"   was replaced by   "m^3". 

Step  1  :

Polynomial Roots Calculator :

 1.1    Find roots (zeroes) of :       F(m) = m³-3m+2
Polynomial Roots Calculator is a set of methods aimed at finding values of  m  for which   F(m)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  m  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  2.

 The factor(s) are:

of the Leading Coefficient :  1
 of the Trailing Constant :  1 ,2

 Let us test ....

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that
   m³-3m+2 
can be divided by 2 different polynomials,including by  m-1 

Polynomial Long Division :

 1.2    Polynomial Long Division
Dividing :  m³-3m+2 
                              ("Dividend")
By         :    m-1    ("Divisor")

Quotient :  m²+m-2  Remainder:  0 

Trying to factor by splitting the middle term

 1.3     Factoring  m²+m-2 

The first term is,  m²  its coefficient is  1 .
The middle term is,  +m  its coefficient is  1 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -2 = -2 

Step-2 : Find two factors of  -2  whose sum equals the coefficient of the middle term, which is   1 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  2 
                     m² - 1m + 2m - 2

Step-4 : Add up the first 2 terms, pulling out like factors :
                    m • (m-1)
              Add up the last 2 terms, pulling out common factors :
                    2 • (m-1)
Step-5 : Add up the four terms of step 4 :
                    (m+2)  •  (m-1)
             Which is the desired factorization

Multiplying Exponential Expressions :

 1.4    Multiply  (m-1)  by  (m-1) 

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (m-1)  and the exponents are :
          1 , as  (m-1)  is the same number as  (m-1)¹ 
 and   1 , as  (m-1)  is the same number as  (m-1)¹ 
The product is therefore,  (m-1)⁽¹⁺¹⁾ = (m-1)² 

Final result :

  (m + 2) • (m - 1)2