Evaluate: 5n × 25n-1 ÷ ( 5n-1× 25n-1)
Answers
Answer:
Simplify ————————
-20n - 1
STEP
2
:
Pulling out like terms
2.1 Pull out like factors :
-20n - 1 = -1 • (20n + 1)
Equation at the end of step
2
:
1
125n2 - ————————
-20n - 1
STEP
3
:
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using (-20n-1) as the denominator :
125n2 125n2 • (-20n - 1)
125n2 = ————— = ——————————————————
1 (-20n - 1)
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
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
-20n - 1 = -1 • (20n + 1)
Adding fractions that have a common denominator :
4.2 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:
125n2 • (-20n-1) - (1) -2500n3 - 125n2 - 1
—————————————————————— = ———————————————————
1 • (-20n-1) 1 • (-20n - 1)
STEP
5
:
Pulling out like terms :
5.1 Pull out like factors :
-2500n3 - 125n2 - 1 = -1 • (2500n3 + 125n2 + 1)
STEP
6
:
Pulling out like terms :
6.1 Pull out like factors :
-20n - 1 = -1 • (20n + 1)
Polynomial Roots Calculator :
6.2 Find roots (zeroes) of : F(n) = 2500n3 + 125n2 + 1
Polynomial Roots Calculator is a set of methods aimed at finding values of n for which F(n)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers n 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 2500 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1,2 ,4 ,5 ,10 ,20 ,25 ,50 ,100 ,125 , etc
of the Trailing Constant : 1
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -2374.00
-1 2 -0.50 -280.25
-1 4 -0.25 -30.25
-1 5 -0.20 -14.00
-1 10 -0.10 -0.25
Note - For tidiness, printing of 15 checks which found no root was suppressed
Polynomial Roots Calculator found no rational roots
Final result :
-2500n3 - 125n2 - 1
———————————————————
-20n - 1