Alright, so this problem has been bothering me for a few days. I've asked three friends for their input, and they're just as stumped as me. I came across this problem in a "college algebra" practice book. What I mean by "this problem has been bothering me" isn't that I'm stuck/haven't found the solution; I've found the solution, it just doesn't seem to work, algebraically. After "solving" the problem, I referred to the solution in the book, and the author did the exact same thing as me. The issue I'm having, like I said, is that the solution to this problem (apparently, as far as I know) does not work algebraically.(adsbygoogle = window.adsbygoogle || []).push({});

Given the following equation, evaluate the expression a + 3b + 2c

2(x^2 - 4x + a)-3(-2x^2 + bx - 1)+5(cx^2 + 5x + 6)=23x^2 + 17x - 5

As far as I know, if you perform an operation on a term on the opposite side of an equation, you must perform that same operation on every term on the opposite side of the equation; to keep the equation "balanced." The (apparent) solution to this problem requires you to basically selectively/sequentially divide terms on the right side, by the corresponding term on the left side to find values for a, b and c. So, algebraically, the solution to this (again, as far as I know) does not seem to work. I'm hoping someone can enlighten me here.

2(x^2 - 4x + a)-3(-2x^2 + bx - 1)+5(cx^2 + 5x + 6)=23x^2 + 17x - 5

After distributing 2, -3, and 5 to the appropriate quantities, combining like-terms and reorganizing/grouping the terms according to the order they appear on the right side, I get:

(5cx^2 + 8x^2)+(-3bx + 17x)+(2a + 33)=23x^2 + 17x - 5

The next step I take is to combine the non-abc terms on the left, with the corresponding terms on the right. So I end up with:

5cx^2 - 3bx + 2a=15x^2 + 0x - 38

(I realize you don't normally write 0x, I just chose to do so in an attempt to illustrate more clearly what I'm trying to do here)

Next, keeping the ordering of the right side of the equation in mind, I divided 5cx^2 by itself to isolate c, and then divided 15x^2 by 5x^2 to get 3. Then -3bx by itself to isolate b, and obviously anything divided by 0=0, so moving onto a. I divided 2a by itself to isolate a and then -38/2 = -19. So:

a=-19

b=0

c=3

Plugging the numbers into the original "evaluate the expression a + 3b + 2c" I end up with a + 3b + 2c = -13. Basically, I just want to know why this solution works, because it seems to contradict my current understanding of algebra. Any help is greatly appreciated! Thanks.

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# Homework Help: Polynomial-related question (why does this work algebraically?)

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