Help with "Proof of Identities and Equalities" Please!
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Help with "Proof of Identities and Equalities" Please!

[From: ] [author: ] [Date: 11-04-30] [Hit: ]
-7 = - 8 + c ==> c = 1.So the solution is a = -2, b = 3, c = 1.......
not sure how to do this problem.
x^3-6x^2+15x-7=(x+a)^3+bx+c <-- need to find what "a","b", and "c" are. Thank you if you can help me out!

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Well, (x + a)^3 = x^3 + 3x²a + 3a²x + a^3. Since you need this part to include both the x^3 and the x² term, you have no choice but to insist that -6x² = 3x²a. This makes a = -2. Absorb the rest into b and c.

x^3 - 6x² + 15x - 7 = (x - 2)^3 + bx + c

x^3 - 6x² + 15x - 7 = x^3 - 6x² + 12x - 8 + bx + c ==>

15x = (12 + b)x ==> b = 3

-7 = - 8 + c ==> c = 1.

So the solution is a = -2, b = 3, c = 1.
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