Answer:
18 is the GCF
Step-by-step explanation:
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
The common ratio of both the formulas is 3 and 2. The first formula is explicit and the second is the recursive formula.
<h3>What is the recursive rule?</h3>
A rule is defined such that its definition includes itself.
1.
The given sequence is
-2, -6, -18, -54
Common ratio ;
r = -6 / -2 = 3
This given formula is the explicit formula.
2.
The given sequence is
4, 8, 16, 32
Common ratio ;
r = 8 / 4 = 2
This given formula is the recursive formula.
Learn more about the recursive rule and explicit rules here:
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we have
we know that
<u>The Rational Root Theorem</u> states that when a root 'x' is written as a fraction in lowest terms
p is an integer factor of the constant term, and q is an integer factor of the coefficient of the first monomial.
So
in this problem
the constant term is equal to
and the first monomial is equal to -----> coefficient is
So
possible values of p are
possible values of q are
therefore
<u>the answer is</u>
The all potential rational roots of f(x) are
(+/-),(+/-),(+/-),(+/-),(+/-),(+/-)
Assuming the order does not matter, you want the number of combinations of 9 things taken 5 at a time. The combinations can be shown as C(9,5), 9C5.
C(9, 5) =
9/5(9-5) =
9*8*7*6*5 / 5*4
The 5 terms cancel.
9*8*7*6 / 4*3*2 =
9*7*2 =
126
The above change is because 4*2 cancels the 8 in the numerator and 6/3 = 2
Therefore, the solution is 126.