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

8252 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve (x+2)/3x + (x-2)/2x = 3


Solve this set of simultaneous equations. 1. 4x+2y=12 2. 2x+3y=10


How to solve a quadratic equation?


How do I know which trig formula to use in the exam?


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