c is a positive integer. Prove that (6c^3 + 30c) / (3c^2 +15) is an even number.
-
We aim to factorise the numerator. This would give 6c(c^2 + 5).
-
We then factorise the denominator. This would give 3(c^2 + 5).
-
Since (c^2 + 5) is present in both the numerator and denominator, it will cancel.
-
This leaves us with 6c/3, which simplifies to 2c.
-
This is an even number because 2 times a positive integer would give an even number.
OB
Related Maths GCSE answers
All answers ▸How do you complete the square for the question x^2 + 6x - 10 ?
Draw the graph of y=2-3x for values of x from -3 to 3.
The perimeter of a right-angled triangle is 72 cm. The lengths of its sides are in the ratio 3 : 4 : 5 Work out the area of the triangle.
Multiply out and simplify (x+7)(x-3)