Simplify x4 - 81 x2 - 9

Step-by-step explanation:

Step by Step Solution:

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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  1 more similar replacement(s).

STEP

1

:

           x4 - 81

Simplify   ———————

           x2 - 9  

Trying to factor as a Difference of Squares:

1.1      Factoring:  x4 - 81  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 81 is the square of 9

Check :  x4  is the square of  x2  

Factorization is :       (x2 + 9)  •  (x2 - 9)  

Polynomial Roots Calculator :

1.2    Find roots (zeroes) of :       F(x) = x2 + 9

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  9.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,3 ,9

Let us test

 P    Q    P/Q    F(P/Q)    Divisor

     -1       1        -1.00        10.00      

     -3       1        -3.00        18.00      

     -9       1        -9.00        90.00      

     1       1        1.00        10.00      

     3       1        3.00        18.00      

     9       1        9.00        90.00      

Polynomial Roots Calculator found no rational roots

Trying to factor as a Difference of Squares:

1.3      Factoring:  x2 - 9  

Check : 9 is the square of 3

Check :  x2  is the square of  x1  

Factorization is :       (x + 3)  •  (x - 3)  

Trying to factor as a Difference of Squares:

1.4      Factoring:  x2 - 9  

Check : 9 is the square of 3

Check :  x2  is the square of  x1  

Factorization is :       (x + 3)  •  (x - 3)  

Canceling Out :

1.5    Cancel out  (x + 3)  which appears on both sides of the fraction line.

Canceling Out :

1.6    Cancel out  (x - 3)  which appears on both sides of the fraction line.

Final result :

 x2 + 9

answer: okw

step-by-step explanation:

2nd one in the first row is correct