according to: https://www.tiger-algebra.com/drill/41u2-(-2u8)/
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "u8" was replaced by "u^8". 1 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
(41 • (u2)) - (0 - 2u8)
STEP
2
:
Equation at the end of step
2
:
41u2 - -2u8
STEP
3
:
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
2u8 + 41u2 = u2 • (2u6 + 41)
Trying to factor as a Sum of Cubes:
4.2 Factoring: 2u6 + 41
Theory : A sum of two perfect cubes, a3 + b3 can be factored into :
(a+b) • (a2-ab+b2)
Proof : (a+b) • (a2-ab+b2) =
a3-a2b+ab2+ba2-b2a+b3 =
a3+(a2b-ba2)+(ab2-b2a)+b3=
a3+0+0+b3=
a3+b3
Check : 2 is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes
Polynomial Roots Calculator :
4.3 Find roots (zeroes) of : F(u) = 2u6 + 41
Polynomial Roots Calculator is a set of methods aimed at finding values of u for which F(u)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers u 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 2 and the Trailing Constant is 41.
The factor(s) are:
of the Leading Coefficient : 1,2
of the Trailing Constant : 1 ,41
Let us test
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 43.00
-1 2 -0.50 41.03
-41 1 -41.00 9500208523.00
-41 2 -20.50 148440798.53
1 1 1.00 43.00
1 2 0.50 41.03
41 1 41.00 9500208523.00
41 2 20.50 148440798.53
Polynomial Roots Calculator found no rational roots
Final result :
u2 • (2u6 + 41)