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Alan51q wrote:The answer, according to the book, is -9. However, I just can't figure out how to get there. Here is the problem:
Find the sum of a, b, c, and d if:
(x^3 - 2x^2 + 3x + 5)/(x+2) = ax^2 + bx + c + d/(x+2)
I figured since this is a synthetic division chapter that I should probably start there, so I used it on the left side of the problem to figure out, I think, that:
x^2 - 4x + 11 + 17/(x+2) = ax^2 + bx + c + d/(x+2)
Alan51q wrote:I wasn't sure how to proceed from there...
Check your signs. I'm pretty sure the fraction should be subtracted instead of added.
Once you have "x^2 - 4x + 11 - 17/(x+2) = ax^2 + bx + c + d/(x+2)", do what they call "equating coefficients": the variables and fraction parts are all the same (after the division) so the coefficients have to be the same. So x^2 = 1x^2 = ax^2, so it has to be a = 1. Etc. Get all the coefficients. Then add them up.