Partial fractions

If we had:

$9x^4 - 27x^3 - 2x^2 + 26x + 35 \equiv (Ax+b)(3x+1)(x-2)^2 ...$ and we were comparing coefficients to get A and B
I understand why A is 3 but I don't understand how they got

-27 = 3B - 12A + A, did they multiply out the brackets and add the x^3 terms or is there another way?

Thanks

That is exactly what they did - that is what comparing coefficients does

So if I multiply out e.g. the $(x-2)^2$ do I still multiply the 4x term from that with two other x terms to get another x^3 term? Sorry if that's worded badly I'll try clarify if it is

yes you do (if I read correctly)

Oh okay thanks! (I need to get faster at expanding, this would take me quite some time in an exam making sure I don't make any errors )

First
Square the (x-2)
Multiply the 2 linears
You know what you are expecting

Then
Multiply the 2 quadratics
You know that you have 3 terms by 3 terms so you know you are looking for 9 terms

I tend to multiply be the first term
Then when multiplying by the second term write those elements under the other line matching terms
etc

The makes things easier to see

Isn't the (x-2) already squared? Do In square them again?

You have lost me

I was trying to help you with a systematic approach to expansion

Where you wrote first square the (x-2) isn't that already squared?

I do not know what you are asking me

Clearly (x-2) has not yet been squared

That is exactly what they did - that is what comparing coefficients does

So which (x-2) am I squaring?

That gives b=2 but putting x=0 gives b=35/4. How is this?

That gives b=2 but putting x=0 gives b=35/4. How is this?

The worked example gives what I quoted and b = 2 :O

is the working out incorrect?

The question is completely wrong

(x-2) is not even a factor

Neither is (3x+1)

Ohh, they somehow still managed to give the solutions:

They gave
A = 3
B = 2
C = 5
D = 1
E = -3

Is that a COMPLETELY different question

You have no C, D, or E in your question in the OP

Ohh sorry I think I've confused everything

I didn't post the original question, I posted part of the working out because I wanted to clarify how to work out B, I didn't think the rest of it would have mattered

Original question was:

$\frac{9x^4 - 27x^3 - 2x^3 + 26x +35}{(x-2)^2 (3x+1)}$