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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