Question

What are the steps to (3w^3+7^2-4w+3) and (w+3)

Answer 1

Equation at the end of step  1  : Step  2  :Equation at the end of step  2  : Step  3  : 3w3 + 7w2 - 4w + 3 Simplify /  w + 3 Checking for a perfect cube :

 3.1    3w3 + 7w2 - 4w + 3  is not a perfect cube

Trying to factor by pulling out :

 3.2      Factoring:  3w3 + 7w2 - 4w + 3 

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

Group 1:  -4w + 3 
Group 2:  3w3 + 7w2 

Pull out from each group separately :

Group 1:   (-4w + 3) • (1) = (4w - 3) • (-1)
Group 2:   (3w + 7) • (w2)

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(w) = 3w3 + 7w2 - 4w + 3
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  3.

 The factor(s) are:

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

 Let us test ....

  P   Q   P/Q   F(P/Q)    Divisor     -1     1      -1.00      11.00        -1     3      -0.33      5.00        -3     1      -3.00      -3.00        1     1      1.00      9.00        1     3      0.33      2.56        3     1      3.00      135.00   

Polynomial Roots Calculator found no rational roots

Polynomial Long Division :

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

dividend  3w3 + 7w2 - 4w + 3 - divisor * 3w2   3w3 + 9w2     remainder  - 2w2 - 4w + 3 - divisor * -2w1   - 2w2 - 6w   remainder      2w + 3 - divisor * 2w0       2w + 6 remainder      - 3 

Quotient :  3w2 - 2w + 2 
Remainder :  -3 

Final result : 3w3 + 7w2 - 4w + 3 over w + 3