Question

(x^2-1)^2+8x(x^2+1)+19x^2 factor

Answer 1

x2-1)2+8x(x2+1)+19x2 Final result : x4 + 8x3 + 17x2 + 8x + 1

Step by step solution :Step  1  :Equation at the end of step  1  : ((((x2)-1)2)+(8x•((x2)+1)))+19x2 Step  2  :Polynomial Roots Calculator :

 2.1    Find roots (zeroes) of :       F(x) = x2+1
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  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  1. 

 The factor(s) are: 

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

 Let us test ....

  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      2.00        1     1      1.00      2.00   


Polynomial Roots Calculator found no rational roots

Equation at the end of step  2  : ((((x2)-1)2)+8x•(x2+1))+19x2 Step  3  :Polynomial Roots Calculator :

 3.1    Find roots (zeroes) of :       F(x) = x4+8x3+17x2+8x+1

     See theory in step 2.1 
In this case, the Leading Coefficient is  1  and the Trailing Constant is  1. 

 The factor(s) are: 

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

 Let us test ....

  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      3.00        1     1      1.00      35.00   


Polynomial Roots Calculator found no rational roots

Final result : x4 + 8x3 + 17x2 + 8x + 1


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