Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (70 • (x4)) +  (24•5x2)
 Step  2  :

Equation at the end of step  2  :

  (2•5•7x4) +  (24•5x2)

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   70x⁴ + 80x²  =   10x² • (7x² + 8) 

Polynomial Roots Calculator :

 4.2    Find roots (zeroes) of :       F(x) = 7x² + 8
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  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  7  and the Trailing Constant is  8.

 The factor(s) are:

of the Leading Coefficient :  1,7
 of the Trailing Constant :  1 ,2 ,4 ,8

 Let us test ....

Polynomial Roots Calculator found no rational roots

Final result :

  10x2 • (7x2 + 8)