The function h(x) = 8x^3 + 7x^5 - x is:

x 3 ⋅(7x 2+8)

Step-by-step explanation:

 (8 • (x3)) +  7x5

 23x3 +  7x5

Pull out like factors :

  7x5 + 8x3  =   x3 • (7x2 + 8)

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

          P      Q         P/Q       F(P/Q)    Diviso

     -1       1        -1.00        15.00    

     -1       7        -0.14        8.14    

     -2       1        -2.00        36.00    

     -2       7        -0.29        8.57    

     -4       1        -4.00        120.00    

     -4       7        -0.57        10.29    

     -8       1        -8.00        456.00    

     -8       7        -1.14        17.14    

     1       1        1.00        15.00    

     1       7        0.14        8.14    

     2       1        2.00        36.00    

     2       7        0.29        8.57    

     4       1        4.00        120.00    

     4       7        0.57        10.29    

     8       1        8.00        456.00    

     8       7        1.14        17.14    

Polynomial Roots Calculator found no rational roots