c is a positive integer. Prove that (6c^3 + 30c) / (3c^2 +15) is an even number.

  1. We aim to factorise the numerator. This would give 6c(c^2 + 5).

  2. We then factorise the denominator. This would give 3(c^2 + 5).

  3. Since (c^2 + 5) is present in both the numerator and denominator, it will cancel.

  4. This leaves us with 6c/3, which simplifies to 2c.

  5. This is an even number because 2 times a positive integer would give an even number.

OB
Answered by Oliver B. Maths tutor

8305 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Part 1 of a test has 60 marks, Part 2 has 100 marks. James scores 75% on part 1 and 48% on part 2. To pass the full test, he needs 60% of the total marks, does he pass?


Find y and x of the to following equations: x +3y = 11 and x + 2y = 9.


Use completing the square to find the minimum of y = x^2 - 4x + 8


Expand the brackets and simplify: 7(2x+3y)-x(14-y)


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences