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How do you do algebraic long division?

To find the quotient and remainder of an algebraic division we use a technique similar to long division at GCSE. I think the best and easiest way to learn this method is to go through an example. See the whi...
NB
Answered by Niamh B. • Maths tutor
5047 Views

Integrate (tanx)^2

Method: We use the trigonometric identity (tanx)^2 +1 = (secx)^2 to understand that (tanx)^2 can be written as (secx)^2-1.We then use the formula booklet to identify that (secx)^2 is a given integral and its...
TD
Answered by Tutor382317 D. • Maths tutor
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Given an integral of a function parametrized with respect to an integer index n, prove a given recursive identity and use this to evaluate the integral for a specific value of n.

This exercise is interesting as it combines a variety of concepts fundamental to integration and maths in general. It also allows to introduce the student to the idea of recursion , very often used to solve ...
MC
Answered by Marco C. • Maths tutor
3013 Views

You are given that n is a positive integer. By expressing (x^2n)-1 as a product of factors, prove that (2^2n)-1 is divisible by 3.

X 2n -1 = (x n +1)(x n -1) Therefore we can say 2 2n -1 = (2 n +1)(2 n -1) . As 2 n is always even, a multiple of 3 is always either going to be 1 above or 1 below it, e.g. 3 is one below 4 and 9 is 1 above ...
AL
Answered by Abraham L. • Maths tutor
10048 Views

A circle has equation x^2 + y^2 - 8x - 10y + 5 = 0, find its centre and radius

To find the centre and radius of the circle, you need to get the equation into the form (x - a) 2 + (y - b) 2 = r 2 . You can do this by rearranging to bring the x and y parts together, and completing the sq...
MB
Answered by Martha B. • Maths tutor
8708 Views