Question

What is the steps to get x^2-5x^3

Answer 1

The way to get to x^2-5x^3 is  1.1    x3-x2-5x-3  is not a perfect cube Trying to factor by pulling out :

 1.2      Factoring:  x3-x2-5x-3 

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

Group 1:  -5x-3 
Group 2:  x3-x2 

Pull out from each group separately :

Group 1:   (5x+3) • (-1)
Group 2:   (x-1) • (x2)

Bad news !! Factoring by pulling out fails : 

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(x) = x3-x2-5x-3
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  1  and the Trailing Constant is  -3. 

 The factor(s) are: 

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