Like so:
.
First, divide each term by 2 to get:
x2 + 3x - 40 = 0
Then factor this to get:
(x - 5)(x + 8) = 0
So the possible solutions are: x = 5 and x = -8
When the two are equal then n = 6, so n+7 = 2n+1 = 13. Since 13 is prime this is the gcd. It is easy to check that smaller values of n result in a gcd of 1.
"A Senate committee has 8 Republicans and 6 Democrats. In how many ways can we form a subcommittee of 5 members that has at least one member from each party?"
When n is an odd number the gcd is 1. When it is an even number the gcd alternates between 2 and 4.
Hence there are three possible gcds: 1, 2 and 4. I'm sure you can add these up yourself!
4 is the greatest common factor:
You could also do it this way:
5 = (x3 - 2x2 -8x)/(x + 2)
5 = x(x + 2)(x - 4)/(x+2)
5 = x(x - 4)
x2 - 4x - 5 = 0
(x + 1)(x - 5) = 0
x = -1 or x = 5
It isn't k that is 14. k is 392.
There are 26 black cards and two red Kings, making 28 cards in total. The probability of choosing one of these from all 52 cards is 28/52 or 7/13 ≈ 0.538
The straight lines around 1-y mean "take the absolute value of". The absolute value of 1-y is the same as that of y-1, so, as Max noted, ln(|y-1|) is the same as ln(|1-y|).
+33669 
