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Here, f(x)=x³e^2x is a function consisting of two functions multiplied together, so we need to use the product rule. The product rule is as follows: where f(x)=u(x)v(x), f'(x)=u(x)v'(...

Factorise both parts of the question. Our left side would become x(2x+3)/(2x+3)(x-2) and our right side would become 6/(x+1)(x-2). On our LHS the (2x+3) would cancel leaving x/x-2. In order to merge the f...

Normally, this would be quite hard! We'd have to play around with the sequence and try different formulas until something worked. Luckily, this is what we call an "Arithmetic Series". That's bec...

By completing the square, since this makes you see that the square will always be >= 0 and the other part allows you to calculate the minima or maxima depending on the sign in front of x². E...

We can work the remainder by using division, and one of the most common methods to use is long division. (Here I would present the method on a whiteboard)

As we can see, the closest multiple of 8 t...