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Firstly the general formula you can use on each of the x terms in the polynomial you are trying to differentiate is; f(x)=xⁿ then f '(x)=nx^n-1 where any constant, c, will differentia...

3a + 12 = ac + 5f 3a - ac = 5f - 12 a(3-c) = 5f - 12 a = (5f - 12)/ (3 - c)

Rearrange line into standard form.

y=5/3*x +1 

For parallel lines the gradient is the same therefore m = 5/3

Point of intersection is where two lines equal eachother

multiply o...

This is a step above a partial fraction question seen in core 1 and core 2, made mkre difficult due to the double (repeated) root of x. To solve this we must consider that there is 3 separate roots, x, x^...

In a question asking us to simplify, we know that our task is to reduce the number of terms presented as far as possible. We should begin inside the brackets by attempting to express both our numbers, 3 a...