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What is the largest positive integer that always divides n^5-n^3 for n a natural number.

First we note we can factorise the n^3 out of the expression, giving n^3(n^2-1). Secondly, we can see that the second term is a difference of two squares, allowing is to factorise the total to n^3(n-1)(n+1)....
WV
Answered by Ward V. • STEP tutor
6168 Views

How can you find the coefficients of a monic quadratic when you know only one non-real root?

We know that non-real roots appear in complex conjugate pairs. Hence when we know one root, we know both of them. Then, as we can factorise a quadratic in it's linear factors, we know our quadratic is a cons...
WV
Answered by Ward V. • Maths tutor
4674 Views

How can 'Natural Moral Law' be critiqued as an ethical theory?

‘Natural Moral Law’ was perhaps most famously developed by St. Thomas Aquinas, in his theological guide ‘Summa Theologica’. Aquinas’ ‘Natural Moral Law’ is an absolutist and deontological ethical approach – ...
EM
10549 Views

At what time did Jane Austen write?

During the Victorian period in English Literary Scene.
AP
2203 Views

How do I make a '5-minute plan' for my essays, and how does that change when I do different questions?

There are two distinct questions here: the first is the important things to bear in mind when planning out your essays in exams, and the second is how your 'template' might change depending on the kind of qu...
EW
Answered by Edward W. • History tutor
4115 Views