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Q: When 3n divided by 7 the remainder is 4 What is the remainder when 2n is divided by 7?

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-3n+5n+4 = -4 2n = -4-4 2n = -8 n = -4

If the number has a remainder of 2 or 4 when divided by 6, it is an even number, so it is not prime number. 6n + 2 = 2 (3n + 1), so it is divisible by 2. 6n + 4 = 2 (3n + 2), so it is divisible by 2. If the number has a remainder of 3 when divided by 6, it is divisible by 3, so it is not a prime number. 6n + 3 = 3 (2n + 1), so it is divisible by 3. However, there are two prime numbers that do not have a remainder of 1 or 5 when divided by 6 : 2 and 3

(2n + 1)(3n - 4)

3n+3=n+7 3n+3-n=n+7-n (subtract n from both sides) 2n+3=7 2n+3-3=7-3 (subtract 3 from both sides ) 2n=4 2n/2=4/2 (divided by 2 on both the sides) n=2 Answer: n=2

3n^4 divided by 3n^3 = n

It is a binomial, which is also a polynomial.

59

74 divided by 5 equals 14 with a remainder of 4

You cannot, because there is no solution.5 is not a factor of 144. Therefore 5 is not a factor of (3n + 9)! / (2n + 4)!Therefore (3n + 9) - (2n + 4) < 5n < 0.Also, 2n + 4 must be non-negative.ie 2n >= -4 or n >= -2.So the only possible values for n are -1 and -2.But n = -1 gives 6!/2! = 720/2 = 360while n = -2 gives 3!/0! = 6

17 divided by 4 is 4 with remainder 1.

212

3n + 9 = 3(n + 3)

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