Solution - Simplification or other simple results

Step  1  :

Trying to factor as a Difference of Squares :

 1.1      Factoring:  m⁴-16 

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 : 16 is the square of 4
Check :  m⁴  is the square of  m² 

Factorization is :       (m² + 4)  •  (m² - 4) 

Polynomial Roots Calculator :

 1.2    Find roots (zeroes) of :       F(m) = m² + 4
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  4.

 The factor(s) are:

of the Leading Coefficient :  1
 of the Trailing Constant :  1 ,2 ,4

 Let us test ....

Polynomial Roots Calculator found no rational roots

Trying to factor as a Difference of Squares :

 1.3      Factoring:  m² - 4 

Check : 4 is the square of 2
Check :  m²  is the square of  m¹ 

Factorization is :       (m + 2)  •  (m - 2) 

Final result :

  (m2 + 4) • (m + 2) • (m - 2)