Mentallic
Jun26-09, 09:43 AM
I'm having trouble understanding what the numerator needs to be in the partial fractions.
e.g.
\frac{1}{(x-1)(x-2)^2}\equiv \frac{A}{x-1}+\frac{Bx+C}{(x-2)^2}
Notice how the first numerator has a constant A, while the second is linear Bx+C.
Actually... just now I think I may understand it. Does it have to do with the fact that during synthetic division, the remainder is always 1 degree less than the divisor? The second fraction's denominator is a quadratic, so its numerator should be linear?
e.g.
\frac{1}{(x-1)(x-2)^2}\equiv \frac{A}{x-1}+\frac{Bx+C}{(x-2)^2}
Notice how the first numerator has a constant A, while the second is linear Bx+C.
Actually... just now I think I may understand it. Does it have to do with the fact that during synthetic division, the remainder is always 1 degree less than the divisor? The second fraction's denominator is a quadratic, so its numerator should be linear?