x^2+1/x^2-11
IT IS OF FACTORISATION
Answers
STEP
1
:
1
Simplify ——
x2
Equation at the end of step
1
:
1
((x2) + ——) - 11
x2
STEP
2
:
Rewriting the whole as an Equivalent Fraction :
2.1 Adding a fraction to a whole
Rewrite the whole as a fraction using x2 as the denominator :
x2 x2 • x2
x2 = —— = ———————
1 x2
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x2 • x2 + 1 x4 + 1
——————————— = ——————
x2 x2
Equation at the end of step
2
:
(x4 + 1)
———————— - 11
x2
STEP
3
:
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using x2 as the denominator :
11 11 • x2
11 = —— = ———————
1 x2
Polynomial Roots Calculator :
3.2 Find roots (zeroes) of : F(x) = x4 + 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
Adding fractions that have a common denominator :
3.3 Adding up the two equivalent fractions
(x4+1) - (11 • x2) x4 - 11x2 + 1
—————————————————— = —————————————
x2 x2
Trying to factor by splitting the middle term
3.4 Factoring x4 - 11x2 + 1
The first term is, x4 its coefficient is 1 .
The middle term is, -11x2 its coefficient is -11 .
The last term, "the constant", is +1
Step-1 : Multiply the coefficient of the first term by the constant 1 • 1 = 1
Step-2 : Find two factors of 1 whose sum equals the coefficient of the middle term, which is -11 .
-1 + -1 = -2
1 + 1 = 2
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
x4 - 11x2 + 1
—————————————
x2