Question

Divide a^3-1bya^2+a+1

Answer 1

Final result :

a3 - a2 + a + 1

Step by step solution :

Step  1  :

Checking for a perfect cube :

 1.1    a3-a2+a+1  is not a perfect cube 

Trying to factor by pulling out :

 1.2      Factoring:  a3-a2+a+1 

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

Group 1:  a+1 
Group 2:  a3-a2 

Pull out from each group separately :

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

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

Polynomial Roots Calculator :

 1.3    Find roots (zeroes) of :       F(a) = a3-a2+a+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 ....

  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      -2.00        1     1      1.00      2.00   


Polynomial Roots Calculator found no rational roots

Final result :

a3 - a2 + a + 1


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