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I was working through some algebra problems when I stumbled across a few that I couldn't solve.

 

1. Let  be a polynomial such that \(f(0) = 4, f(1) = 5,\)  and \(f(2) = 10\). Find the remainder when \(f(x)\) is divided by \(x(x - 1)(x - 2).\)

 

2. Let \(f(x) = x^{10}+5x^9-8x^8+7x^7-x^6-12x^5+4x^4-8x^3+12x^2-5x-5\).

Without using long division, find the remainder when \(f(x)\) is divided by \(x^2-1\).

 

Thank you very much for your help!

 Jul 26, 2020
 #1
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Thank you very much for giving us your homework!

 Jul 26, 2020
 #2
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This is not my homework as I am on summer vacation.

 Jul 26, 2020
 #3
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1. By long division, the remainder is x^2 + 4x - 3.

 

2. By long division, the remainder is 7x - 2.

 Jul 26, 2020
 #4
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I tried those answers and they were incorrect. Do you have any idea where you went wrong?

 Jul 26, 2020

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