Question

3x3 + 9x2 + x + 3 factor completely

Answer 1

30 + x  thats yhur answer

or

(3x2 + 1) • (x + 3)

Reformatting the input :

Changes made to your input should not affect the solution:

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

Step by step solution :Equation at the end of step  1  : (((3 • (x3)) + 32x2) + x) + 3 Step  2  :Equation at the end of step  2  : ((3x3 + 32x2) + x) + 3 Step  3  :Checking for a perfect cube :

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

Trying to factor by pulling out :

 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

Polynomial Roots Calculator :

 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 ....

  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      4.00        -1     3      -0.33      1.33        1     1      1.00      4.00        1     3      0.33      1.33   

Polynomial Roots Calculator found no rational roots

Final result : (3x2 + 1) • (x + 3) thats yhur answer

Processing ends successfully

im not sure wich one yhu need