Use induction to prove: for every integer n > 1, the number n5 - n is a multiple of 5.

we need to prove : for every integer n>1, the number is a multiple of 5.

1) check divisibility for n=1,  (divisible)

2) Assume that is divisible by 5,

3) Induction,

Now,

Take out the common factor,

     (divisible by 5)

add both the sides by f(k)

We have proved that difference between and is divisible by 5.

so, our assumption in step 2 is correct.

Since is divisible by 5, then must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number is a multiple of 5.

the correct answer option is (2x-3)(2x+3).

step-by-step explanation:

we are given the following expression and we are to factorize it:

we are to find such factors that when multiplied they give a result of 36 (9 x 4 = 36) and when added they give a result of 0.

the two such factors of 36 are negative six and postive six.

factorizing the given expression to get:

therefore, the correct factorization of is (2x-3)(2x+3).