Question

5a⁴- 3a² + a⁴ + 4a²​

Answer 1

Respuesta:5a4-3a2+a4+4a2  

Final result :

 a2 • (6a2 + 1)

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "a4"   was replaced by   "a^4".  1 more similar replacement(s).

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (((5•(a4))-(3•(a2)))+(a4))+22a2

Step  2  :

Equation at the end of step  2  :

 (((5 • (a4)) -  3a2) +  a4) +  22a2

Step  3  :

Equation at the end of step  3  :

 ((5a4 -  3a2) +  a4) +  22a2

Step  4  :

Step  5  :

Pulling out like terms :

5.1     Pull out like factors :

  6a4 + a2  =   a2 • (6a2 + 1)  

Polynomial Roots Calculator :

5.2    Find roots (zeroes) of :       F(a) = 6a2 + 1

Polynomial Roots Calculator is a set of methods aimed at finding values of  a  for which   F(a)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  a  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  6  and the Trailing Constant is  1.

The factor(s) are:

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

of the Trailing Constant :  1

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        7.00      

     -1       2        -0.50        2.50      

     -1       3        -0.33        1.67      

     -1       6        -0.17        1.17      

     1       1        1.00        7.00      

     1       2        0.50        2.50      

     1       3        0.33        1.67      

     1       6        0.17        1.17      

Polynomial Roots Calculator found no rational roots

Final result :

 a2 • (6a2 + 1)

Processing ends successfully

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Answer 2

Respuesta:

.........

Explicación paso a paso: