Solve some partial fractions

Hi, here are some questions you can try to put your skills on partial fraction to good use.

Eamil me (liauteach@gmail.com) for the worked solutions.

Colourful Covers

Today's post is with regards to the topic on Partial Fractions.

One way of finding the unknown numerators in partial fractions is to use the cover-up rule, which I will demonstrate.

Note: the example used involves an improper fraction (numerator smaller than denominator) with distinct linear factors.
Linear meaning the highest power of x is only one, there is no x square or x cube.
Factors of a quadratic (or any other polynomial equation) in the case below, (x+2)(x-2) are factors of

Synthetic or Organic?

No we are not talking about food or hair products. We are discussing a quick and nifty way to solving polynomial equations.

I shall not waste your time, so let's get down to solving this.

There are 3 methods to solving this; the first part is the same for all 3 methods. You try random values of x, such as -1, 0 or 1 and see which gets you zero.

In this case, if you used x=1, then 2+5-11+4=0. And wah la!, (x-1) is a factor.

Note: if you subbed x=? and that ? makes your equation ZERO, then (x-?) is a factor.

Now this is where things start to differ.

Method 1: Solving by Long division

Method 2: Synthetic

The solution is, x=1 or x=1/2 or x=-4 (Ans)

Headstart to A

Have you ever wondered why you just couldn’t motivate yourself to score that A you desire?

I guess it’s because you find the task of getting that desired grade daunting. You look around you and notice that hey!, many of your friends are like you. You then begin to feel safe as you realise you are part of a majority. What makes matters worse, is that, those who score, are totally unlike you; you can never imagine yourself being like them.

Here are 5 things you can do to change that mindset and learn Math the way you like it.

1. Set aside a little time a day to visit this blog, challenge your mind and attempt the questions

2. Share this blog with your friends and talk about that math question you could, or could not solve at night

3. Be bold and start asking for help when you encounter difficulty. You can consult your teachers at school or send me an email at liauteach@gmail.com

4. Look for a tutor you can relate with; one who can make you passionate and excited about math

5. DO NOT procrastinate, if you cannot do all 5, at least do no. 1.