Answer:
4 • (3x4 + 2)
———————
x2
Step-by-step explanation:
Step 1 :
8
Simplify ——
x2
Equation at the end of step 1 :
8
—— + 12x2
x2
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Adding a whole to a fraction
Rewrite the whole as a fraction using x2 as the denominator :
12x2 12x2 • x2
12x2 = ———— = —————————
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:
8 + 12x2 • x2 12x4 + 8
————————————— = ————————
x2 x2
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
12x4 + 8 = 4 • (3x4 + 2)
Polynomial Roots Calculator :
3.2 Find roots (zeroes) of : F(x) = 3x4 + 2
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 3 and the Trailing Constant is 2.
The factor(s) are:
of the Leading Coefficient : 1,3
of the Trailing Constant : 1 ,2
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 5.00
-1 3 -0.33 2.04
-2 1 -2.00 50.00
-2 3 -0.67 2.59
1 1 1.00 5.00
1 3 0.33 2.04
2 1 2.00 50.00
2 3 0.67 2.59
Polynomial Roots Calculator found no rational roots
Final result :
4 • (3x4 + 2)
—————————————
x2
Processing ends successfully
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