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 Â Â 2m3+6m2+3m+9 Â is not a perfect cube Â
Trying to factor by pulling out :
3.2 Â Â Â Factoring: Â 2m3+6m2+3m+9 Â
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: Â 3m+9 Â
Group 2: Â 6m2+2m3 Â
Pull out from each group separately :
Group 1:  (m+3) • (3)
Group 2:  (m+3) • (2m2)
      Â
Add up the two groups :
       (m+3)  •  (2m2+3) Â
Which is the desired factorization
Polynomial Roots Calculator :
3.3 Â Â Find roots (zeroes) of : Â Â Â F(m) = 2m2+3
Polynomial Roots Calculator is a set of methods aimed at finding values of  m  for which  F(m)=0 Â
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. Â
The factor(s) are: Â
of the Leading Coefficient : Â 1,2 Â
of the Trailing Constant : Â 1 ,3 Â
Let us test
 P   Q   P/Q   F(P/Q)   Divisor
   -1    1     -1.00     5.00   Â
   -1    2     -0.50     3.50   Â
   -3    1     -3.00     21.00   Â
   -3    2     -1.50     7.50   Â
   1    1     1.00     5.00   Â
   1    2     0.50     3.50   Â
   3    1     3.00     21.00   Â
   3    2     1.50     7.50   Â
Polynomial Roots Calculator found no rational roots
Final result :
 (2m2 + 3) • (m + 3)
Processing ends successfully
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