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How do you factorise quadratic, cubic functions or even quartic functions?

Start by trying to find a common multiple of the last term, e.g. if you have a quadratic that ends in 4, when you factorise this function, we should get two terms ending in multiplies of 4 so (1,4) or (2,...

Answered by Nacima M. • Maths tutor

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Let f(x)=xln(x)-x. Find f'(x). Hence or otherwise, evaluate the integral of ln(x^3) between 1 and e.

We use the product rule with u=x and v=ln(x) (so u'=1 andv'=1/x) to differentiate xln(x) to ln(x)+1, and -x just differentiates to -1, hence we have. f'(x)=ln(x).
Now note that ln(x^3)=3ln(x) using p...

Answered by Matthew J. • Maths tutor

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(19x - 2)/((5 - x)(1 + 6x)) can be expressed as A/(5-x) + B/(1+6x) where A and B are integers. Find A and B

First we can equate (19x - 2)/((5 - x)(1 + 6x)) to A/(5-x) + B/(1+6x) which means: (19x - 2)/((5 - x)(1 + 6x)) = A/(5-x) + B/(1+6x). Then we will turn the RHS into a single fraction: (19x - 2)/((5 - x)(1 ...

Answered by Tarek S. • Maths tutor

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If 2 log(x + a) = log(16a^6), where a is a positive constant, find x in terms of a

Use the power rule on the right hand side of the equation to reduce the expression into simpler termsRemoves logs (several methods, I would personally halve and then cancel)Factorise to give x=a(4a^2<...

Answered by Michael L. • Maths tutor

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