(7a^3 - 2α – 2) +(-5a+ 3)

 7a^3 - 7a + 1

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 ((7a3 -  2a) -  2) +  (3 - 5a)

Step  2  :

Polynomial Roots Calculator :

2.1    Find roots (zeroes) of :       F(a) = 7a3-7a+1

Polynomial Roots Calculator is a set of methods aimed at finding values of  a  for which   F(a)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  a  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  1.

The factor(s) are:

of the Leading Coefficient :  1,7

of the Trailing Constant :  1

Let us test

 P    Q    P/Q    F(P/Q)    Divisor

     -1       1        -1.00        1.00    

     -1       7        -0.14        1.98    

     1       1        1.00        1.00    

     1       7        0.14        0.02    

Hope this helped :)