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
