Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x3"   was replaced by   "x^3".  4 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  ((((7•(x8))-(7•(x3)))+(7•(x2)))+8)+(((7•(x7))+22x3)-2x)
 Step  2  :

Equation at the end of step  2  :

  ((((7•(x8))-(7•(x3)))+(7•(x2)))+8)+((7x7+22x3)-2x)
 Step  3  :

Equation at the end of step  3  :

  ((((7•(x8))-(7•(x3)))+7x2)+8)+(7x7+4x3-2x)
 Step  4  :

Equation at the end of step  4  :

  ((((7•(x8))-7x3)+7x2)+8)+(7x7+4x3-2x)
 Step  5  :

Equation at the end of step  5  :

  (((7x8 -  7x3) +  7x2) +  8) +  (7x7 + 4x3 - 2x)

Step  6  :

Trying to factor by pulling out :

 6.1      Factoring:  7x⁸+7x⁷-3x³+7x²-2x+8 

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

Group 1:  -3x³+7x² 
Group 2:  7x⁸+7x⁷ 
Group 3:  -2x+8 

Pull out from each group separately :

Group 1:   (3x-7) • (-x²)
Group 2:   (x+1) • (7x⁷)
Group 3:   (x-4) • (-2)


Looking for common sub-expressions :

Group 1:   (3x-7) • (-x²)
Group 3:   (x-4) • (-2)
Group 2:   (x+1) • (7x⁷)

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 :

 6.2    Find roots (zeroes) of :       F(x) = 7x⁸+7x⁷-3x³+7x²-2x+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 :

  7x8 + 7x7 - 3x3 + 7x2 - 2x + 8