Finding unknown constants

**Glitch** · January 7th 2011, 01:29 AM

The question

Find the constants A, B and C for:

$x^2 + 3 = A(x + 1)^2 + B(x - 1)(x + 1) + C(x - 1)$

My attempt
I tried to isolate the constants by substituting strategic values of x. For example:

Let x = -1,
C = -2

Let x = 1,
A = 1

However, I cannot isolate B. I'm sure this question is trivial and my brain is still in holiday mode. Any assistance would be most welcome.

**Random Variable** · January 7th 2011, 01:40 AM

You can expand the stuff on the right and then equate like terms. You'll get a system of equations.

**FernandoRevilla** · January 7th 2011, 01:41 AM

Originally Posted by Glitch

Let x = -1, C = -2 Let x = 1, A = 1

Right. Now, substitute (for example) $x=0$ and find $B$ .

Fernando Revilla

**TheCoffeeMachine** · January 7th 2011, 01:46 AM

Put $x = 0$ and use the values of A and C which you have already found to get B.
Zero is just convenient - any constant apart from those which you have used will do.

EDIT: Oops! Ah, well! I'm too slow, I guess.