Algebraic Proof (AQA GCSE Further Maths)

Show that  is divisible by 9 for all integer values of .

and

Tick the correct box for each statement.

If is positive for all values of , which condition below is correct?

Circle your answer.

Prove that the sum of the squares of three consecutive integers is always two more than a multiple of 3.

, and are three consecutive integers, for all integer values of .

The product of the three consecutive integers is added to the middle integer.

Prove that the result is always a cube number.

Prove that    for all values of .

and are numbers such that

Tick the correct box for each statement.

A function is given by

Prove that, for any input , the function will never give a negative output.