Factor by grouping
2m^3+6m^2+3m+9

Step-by-step explanation:

Final result :

 (2m2 + 3) • (m + 3)

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "m2"   was replaced by   "m^2".  1 more similar replacement(s).

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (((2 • (m3)) +  (2•3m2)) +  3m) +  9

Step  2  :

Equation at the end of step  2  :

 ((2m3 +  (2•3m2)) +  3m) +  9

Step  3  :

Checking for a perfect cube :

3.1    2m3+6m2+3m+9  is not a perfect cube  

Trying to factor by pulling out :

3.2      Factoring:  2m3+6m2+3m+9  

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

Group 1:  3m+9  

Group 2:  6m2+2m3  

Pull out from each group separately :

Group 1:   (m+3) • (3)

Group 2:   (m+3) • (2m2)

Add up the two groups :

              (m+3)  •  (2m2+3)  

Which is the desired factorization

Polynomial Roots Calculator :

3.3    Find roots (zeroes) of :       F(m) = 2m2+3

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  2  and the Trailing Constant is  3.  

The factor(s) are:  

of the Leading Coefficient :  1,2  

of the Trailing Constant :  1 ,3  

Let us test

 P    Q    P/Q    F(P/Q)    Divisor

     -1       1        -1.00        5.00      

     -1       2        -0.50        3.50      

     -3       1        -3.00        21.00      

     -3       2        -1.50        7.50      

     1       1        1.00        5.00      

     1       2        0.50        3.50      

     3       1        3.00        21.00      

     3       2        1.50        7.50      

Polynomial Roots Calculator found no rational roots

Final result :

 (2m2 + 3) • (m + 3)

Processing ends successfully

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