Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "p2"   was replaced by   "p^2".  1 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  ((5•(p3))-p)-((7p2+4p)-3)
 Step  2  :

Equation at the end of step  2  :

  (5p3 -  p) -  (7p2 + 4p - 3)

Step  3  :

Checking for a perfect cube :

 3.1    5p³-7p²-5p+3  is not a perfect cube

Trying to factor by pulling out :

 3.2      Factoring:  5p³-7p²-5p+3 

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

Group 1:  -5p+3 
Group 2:  5p³-7p² 

Pull out from each group separately :

Group 1:   (-5p+3) • (1) = (5p-3) • (-1)
Group 2:   (5p-7) • (p²)

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 :

 3.3    Find roots (zeroes) of :       F(p) = 5p³-7p²-5p+3
Polynomial Roots Calculator is a set of methods aimed at finding values of  p  for which   F(p)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  p  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  5  and the Trailing Constant is  3.

 The factor(s) are:

of the Leading Coefficient :  1,5
 of the Trailing Constant :  1 ,3

 Let us test ....

Polynomial Roots Calculator found no rational roots

Final result :

  5p3 - 7p2 - 5p + 3