<span>Equation at the end of step  1  :</span><span>
<span> Step  2  :</span></span><span>Equation at the end of step  2  :</span>
<span> Step  3  :</span><span> 3w3 + 7w2 - 4w + 3
Simplify /  w + 3
</span>Checking for a perfect cube :
<span> 3.1 </span>  <span> 3w3 + 7w2 - 4w + 3</span>  is not a perfect cube 
Trying to factor by pulling out :
<span> 3.2 </span>     Factoring: <span> 3w3 + 7w2 - 4w + 3</span> 
 Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1:  -4w + 3 
Group 2: <span> 3w3 + 7w2</span> 
Pull out from each group separately :
Group 1:   (-4w + 3) • (1) = (4w - 3) • (-1)
Group 2: <span>  (3w + 7) • (w2)</span>
<span>Bad news !! Factoring by pulling out fails : 
</span>The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
<span> 3.3 </span>   Find roots (zeroes) of :      <span> F(w) = 3w3 + 7w2 - 4w + 3</span>
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  3  and the Trailing Constant is <span> 3. 
 </span>The factor(s) are: 
of the Leading Coefficient : <span> 1,3 
 </span>of the Trailing Constant : <span> 1 ,3 
 </span>Let us test ....
<span><span>  P   Q   P/Q   F(P/Q)    Divisor</span><span>     -1     1      -1.00      11.00   </span><span>     -1     3      -0.33      5.00   </span><span>     -3     1      -3.00      -3.00   </span><span>     1     1      1.00       9.00   </span><span>     1     3      0.33      2.56   </span><span>     3     1      3.00      135.00   </span></span>
Polynomial Roots Calculator found no rational roots 
Polynomial Long Division :
<span> 3.4 </span>   Polynomial Long Division 
 Dividing : <span> <span>3w3 + 7w2 - 4w + 3</span> 
                              ("Dividend")
</span> By         :   <span> w + 3    ("Divisor")
</span>
<span><span>dividend <span> 3w3 </span>+<span> 7w2 </span>- 4w + 3 </span><span>- divisor<span> <span>* 3w2</span> </span> <span> 3w3 </span>+<span> 9w2 </span>    </span><span>remainder  -<span> 2w2 </span>- 4w + 3 </span><span>- divisor<span> <span>* -2w1</span> </span>  -<span> 2w2 </span>- 6w   </span><span>remainder      2w + 3 </span><span>- divisor<span> <span>* 2w0</span> </span>      2w + 6 </span><span>remainder      - 3 </span></span>
 Quotient : <span> <span>3w2 - 2w + 2</span>  
</span> Remainder : <span> -3  
</span>
Final result :<span> 3w3 + 7w2 - 4w + 3 over w + 3
</span>