3x3 + 9x2 + x + 3 factor completely

Changes made to your input should not affect the solution:

 (1): "x2"   was replaced by   "x^2".  1 more similar replacement(s).

 3.1    3x3+9x2+x+3  is not a perfect cube 

 3.2      Factoring:  3x3+9x2+x+3 

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

Group 1:  x+3 
Group 2:  3x3+9x2 

Pull out from each group separately :

Group 1:   (x+3) • (1)
Group 2:   (x+3) • (3x2)
              
Add up the two groups :
               (x+3)  •  (3x2+1) 
Which is the desired factorization

 3.3    Find roots (zeroes) of :       F(x) = 3x2+1
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  3  and the Trailing Constant is  1. 

 The factor(s) are: 

of the Leading Coefficient :  1,3 
 of the Trailing Constant :  1 

 Let us test

Polynomial Roots Calculator found no rational roots

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answer: 0,6

step-by-step explanation:

this would make it the y intercept.