Factor completely.
20x3 + 12x2 + 5x+3
o a. (2x + 1)(5x+3)
ob. (2x + 3)(5x+3)
oc. (4x2 + 1)(x+3)
od. (4x2 + 1)(5x+3)

(5x+3)(4x2+1)

Step-by-step explanation:

20x3-12x2+5x-3

Final result :

 (4x2 + 1) • (5x - 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 :

Step  1  :

Equation at the end of step  1  :

 (((20 • (x3)) -  (22•3x2)) +  5x) -  3

Step  2  :

Equation at the end of step  2  :

 (((22•5x3) -  (22•3x2)) +  5x) -  3

Step  3  :

Checking for a perfect cube :

3.1    20x3-12x2+5x-3  is not a perfect cube

Trying to factor by pulling out :

3.2      Factoring:  20x3-12x2+5x-3

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

Group 1:  5x-3

Group 2:  20x3-12x2

Pull out from each group separately :

Group 1:   (5x-3) • (1)

Group 2:   (5x-3) • (4x2)

Add up the two groups :

              (5x-3)  •  (4x2+1)

Which is the desired factorization

Polynomial Roots Calculator :

3.3    Find roots (zeroes) of :       F(x) = 4x2+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  4  and the Trailing Constant is  1.

The factor(s) are:

of the Leading Coefficient :  1,2 ,4

of the Trailing Constant :  1

Let us test

 P    Q    P/Q    F(P/Q)    Divisor

     -1       1        -1.00        5.00    

     -1       2        -0.50        2.00    

     -1       4        -0.25        1.25    

     1       1        1.00        5.00    

     1       2        0.50        2.00    

     1       4        0.25        1.25    

Polynomial Roots Calculator found no rational roots

Final result :

 (4x2 + 1) • (5x - 3)