Solving Partial Fractions

Q1)

From my understanding, I have to always factorize the denominator of the fraction to one of these 3 formulas to proceed on:

1.

2.

3. where cannot be factored into linear factors (omg i haven't touch on this yet)

However I tried and failed to factorize the denominator to substitute to any of the formulas above.

Please enlighten me! I just need to change them into one of the stated formula and I can to solve it further by myself. Your every effort is appreciated.. Thank you.

Re: Solving Partial Fractions

We have:

Taking the discriminant of the quadratic on the denominator:

This tells us that this quadratic will factor, as is a perfect square (think of the quadratic formula, and what would happen if you substituted).

Soon, we deduce that the factors are by trial and error (fortunately, doesn't give many options).

Can you take it from there?

Edit: I'm sorry you had to wait so long for a response.

Re: Solving Partial Fractions

Thank youfor your help! No worries about the me taken.