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

Our starting equation (6c3+30c) / ( 3c2 +15)  can be factorised by 6c on the top row and 3 on the bottom row so you get 6c(c2+5) / 3(c2+5). Because (c2+5) is on the top and bottom row it can be cancelled out so you have 6c / 3.  This can be further simplified as 6c / 3 can be split into 6/3 x c/1 and because 6/3 = 2 this gives us 2 x c/1 = 2 x c = 2c. Therefore the answer will be a multiple of 2, so the answer will be even.

LA
Answered by Lenya A. Maths tutor

5705 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve the simultaneous equations, (1) 4x+y=23 and (2) 3x+5y=111/2


Work out 2 3/4 x 1 1/2. Give your answer in terms of a mixed fraction in simplest form.


When would I use the quadratic formula?


Line L1 passes through points (4,6) and (12,2). Line L2 passes through the origin and has gradient -3. The two lines intersect at point P. Find the co-ordinates of P.


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