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

Processing ends successfully

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490