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Simplification or other simple results

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We think you wrote:

3y^5-2y^4+18y-12

This solution deals with simplification or other simple results.

Solution found

(y^4+6)*(3y-2)
(y^4+6)*(3y-2)

Step by Step Solution

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Step  1  :

Equation at the end of step  1  :

  (((3 • (y5)) -  2y4) +  18y) -  12

Step  2  :

Equation at the end of step  2  :

  ((3y5 -  2y4) +  18y) -  12

Step  3  :

Checking for a perfect cube :

 3.1    3y5-2y4+18y-12  is not a perfect cube

Trying to factor by pulling out :

 3.2      Factoring:  3y5-2y4+18y-12 

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

Group 1:  18y-12 
Group 2:  3y5-2y4 

Pull out from each group separately :

Group 1:   (3y-2) • (6)
Group 2:   (3y-2) • (y4)
               -------------------
Add up the two groups :
               (3y-2)  •  (y4+6) 
Which is the desired factorization

Polynomial Roots Calculator :

 3.3    Find roots (zeroes) of :       F(y) = y4+6
Polynomial Roots Calculator is a set of methods aimed at finding values of  y  for which   F(y)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  y  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  6.

 
The factor(s) are:

of the Leading Coefficient :  1
 
of the Trailing Constant :  1 ,2 ,3 ,6

 
Let us test ....

  P  Q  P/Q  F(P/Q)   Divisor
     -1     1      -1.00      7.00   
     -2     1      -2.00      22.00   
     -3     1      -3.00      87.00   
     -6     1      -6.00      1302.00   
     1     1      1.00      7.00   
     2     1      2.00      22.00   
     3     1      3.00      87.00   
     6     1      6.00      1302.00   


Polynomial Roots Calculator found no rational roots

Final result :

  (y4 + 6) • (3y - 2)

Why learn this

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Terms and topics

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