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The factors are 2n(4n + 3).
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What is 5 over 2n plus 3 over 3n?
15/6n + 6/6n = 21/6n = 7/2n
Why all non prime number are divisible by 2 or 3 or 6 times n plus 1 or 6 times n minus 1?
All non-prime numbers are divisible by prime numbers. Now the smallest to prime numbers are 2 and 3. The next prime number is 5, which is 6*1 - 1. All larger numbers are in the form of one of 6n, 6n+1, 6n+2, 6n+3, 6n+4, 6n+5. Now 6n is divisible by 2 and so cannot be a prime. 6n+2 and 6n+4 are also divisible by 2 and so cannot be prime. 6n+3 is divisible by 3 and so cannot be prime. That leave 6n+1 and 6n+5 as the only two forms than can be prime. Note though that 6n+5 = 6m-1 where m = n+1. So all primes are of the form 2, 3, 6n+1 and 6n-1. And all primes can be divided by primes. The result follows.
Is there a pattern for prime numbers?
So far, the best and most general pattern found is that, over three, all prime numbers are of the form 6n +/- 1. In other words, they're either 6n - 1 or 6n + 1, for some n. Here is why this is true. We could do a proof by contradiction and assume that all the natural numbers greater than or equal to 5 are prime. (of course they are not!) We start with5 which is 6-1. The numbers would then be 6n - 1, 6n, 6n + 1, 6n + 2, 6n + 3, 6n + 4, and 6n + 5 for some natural number n. If it is 6n, then the number is divisible by 6. When it is 6n + 2, the number is the same as 2(3n+1) so it is divisible by 2. Consider 6n + 3, the number is 3(2n+1), so it is divisible by 3. Last look at 6n + 4, the number is divisible by 2, for it's 2(3n + 2). Therefore all numbers of the form 6n, 6n + 2, 6n + 3, and 6n + 4 are not prime. The only possibilities this leaves are 6n - 1 and 6n + 1. This entire thing can be written more elegantly with congruences, but the goal here was simplicity! There are many other patterns in primes. See the attached link to see them.
What is the general form of prime numbers?
All prime numbers over 3 are either 6n - 1 or 6n + 1.
What are the factors of the following trinomial 2x2 plus 7x plus 3?
(2x + 1)(x + 3) are the factors.
What is 6n plus 5n?
6n + 5n is 11n.
How do you factor 8n2 plus 36n plus 40?
4(n + 2)(2n + 5)
What is the answer to 6mn - mn plus 6n - 14?
5mn + 6n - 14
What is 3n2 minus 5n minus 4n3 plus 5n2 plus n plus 7?
-4n3 + 8n2 - 4n + 7
What is the answer to 6n plus 5 equals 17?
6n = 12 n = 2
How do you evaluate 6n plus 4 and 6n plus 4 for n3?
I assume that you mean n = 3 6n + 4 = 6(3) + 4 = 18 + 4 = 22
What is the equation of -5 equals 6n plus 7?
-5=6n+7 -5-7=6n+7-7 -12=6n -12/6=6n/6 -2=n
What is 4n plus 1 times 2n plus 6?
(4n + 1)*(2n + 6) = 8n2 + 26n + 6
What is 5 over 2n plus 3 over 3n?
15/6n + 6/6n = 21/6n = 7/2n
What is 9m plus 6n-3m plus 7n?
This question as written can be taken two ways: 9m + 6n - 3m + 7n = 6m + 13n, or (9m + 6n) - (3m + 7n) = 9m + 6n - 3m - 7n = 6m - n
What is 12m plus 9n-4-10m plus 6n?
12m + 9n - 4 - 10m + 6n = 2m + 15n - 4
What is the solution to 6n-4-3 equals 3n plus 10 plus 4n?
6n - 4 - 3 = 3n + 10 + 4n -7 = 7n - 6n + 10 -17 = n
