Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  
 Step  2  :

Equation at the end of step  2  :

Step  3  :

            -4w3 + 7w2 - 8
 Simplify   ——————————————
                w - 3     

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   -4w³ + 7w² - 8  =   -1 • (4w³ - 7w² + 8) 

Polynomial Roots Calculator :

 4.2    Find roots (zeroes) of :       F(w) = 4w³ - 7w² + 8
Polynomial Roots Calculator is a set of methods aimed at finding values of  w  for which   F(w)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  w  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  8.

 The factor(s) are:

of the Leading Coefficient :  1,2 ,4
 of the Trailing Constant :  1 ,2 ,4 ,8

 Let us test ....

Polynomial Roots Calculator found no rational roots

Polynomial Long Division :

 4.3    Polynomial Long Division
Dividing :  -4w³ + 7w² - 8 
                              ("Dividend")
By         :    w - 3    ("Divisor")

Quotient :  -4w² - 5w - 15 
Remainder :  -53 

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   -4w³ + 7w² - 8  =   -1 • (4w³ - 7w² + 8) 

Polynomial Roots Calculator :

 5.2    Find roots (zeroes) of :       F(w) = 4w³ - 7w² + 8

     See theory in step 4.2
In this case, the Leading Coefficient is  4  and the Trailing Constant is  8.

 The factor(s) are:

of the Leading Coefficient :  1,2 ,4
 of the Trailing Constant :  1 ,2 ,4 ,8

 Let us test ....

Polynomial Roots Calculator found no rational roots

Final result :

  -4w3 + 7w2 - 8
  ——————————————
      w - 3     

See results of polynomial long division:

1. In step #04.03