No solutions found

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

           16*(o*m*e*g*a+o*m*e*g*a^8)-(-16)=0 

Step  1  :

Step  2  :

Pulling out like terms :

 2.1     Pull out like factors :

   omega⁸ + omega  =   omega • (a⁷ + 1) 

Polynomial Roots Calculator :

 2.2    Find roots (zeroes) of :       F(a) = a⁷ + 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  1  and the Trailing Constant is  1.

 The factor(s) are:

of the Leading Coefficient :  1
 of the Trailing Constant :  1

 Let us test ....

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that
   a⁷ + 1 
can be divided with  a + 1 

Polynomial Long Division :

 2.3    Polynomial Long Division
Dividing :  a⁷ + 1 
                              ("Dividend")
By         :    a + 1    ("Divisor")

Quotient :  a⁶-a⁵+a⁴-a³+a²-a+1  Remainder:  0 

Polynomial Roots Calculator :

 2.4    Find roots (zeroes) of :       F(a) = a⁶-a⁵+a⁴-a³+a²-a+1

     See theory in step 2.2
In this case, the Leading Coefficient is  1  and the Trailing Constant is  1.

 The factor(s) are:

of the Leading Coefficient :  1
 of the Trailing Constant :  1

 Let us test ....

Polynomial Roots Calculator found no rational roots

Equation at the end of step  2  :

  16omega•(a6-a5+a4-a3+a2-a+1)•(a+1)--16  = 0 

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   16omega⁸ + 16omega + 16  =   16 • (omega⁸ + omega + 1) 

Trying to factor a multi variable polynomial :

 4.2    Factoring    omega⁸ + omega + 1 

Try to factor this multi-variable trinomial using trial and error 

 Factorization fails

Equation at the end of step  4  :

  16 • (omega8 + omega + 1)  = 0 

Step  5  :

Equations which are never true :

 5.1      Solve :    16   =  0

This equation has no solution.
A a non-zero constant never equals zero.

Solving a Single Variable Equation :

 5.2     Solve   omega⁸+omega+1  = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

We shall not handle this type of equations at this time.

No solutions found