Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (((3•(a3))-(7•(a2)))+a)-(((6•(a3))-22a2)-8)
 Step  2  :

Equation at the end of step  2  :

  (((3•(a3))-(7•(a2)))+a)-(((2•3a3)-22a2)-8)
 Step  3  :

Equation at the end of step  3  :

  (((3•(a3))-7a2)+a)-(6a3-4a2-8)
 Step  4  :

Equation at the end of step  4  :

  ((3a3 -  7a2) +  a) -  (6a3 - 4a2 - 8)

Step  5  :

Checking for a perfect cube :

 5.1    -3a³-3a²+a+8  is not a perfect cube

Trying to factor by pulling out :

 5.2      Factoring:  -3a³-3a²+a+8 

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  a+8 
Group 2:  -3a³-3a² 

Pull out from each group separately :

Group 1:   (a+8) • (1)
Group 2:   (a+1) • (-3a²)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

 5.3    Find roots (zeroes) of :       F(a) = -3a³-3a²+a+8
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  -3  and the Trailing Constant is  8.

 The factor(s) are:

of the Leading Coefficient :  1,3
 of the Trailing Constant :  1 ,2 ,4 ,8

 Let us test ....

Polynomial Roots Calculator found no rational roots

Final result :

  -3a3 - 3a2 + a + 8