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📰 eq 0 $. Contradiction? Wait, from $ k(2) = 0 $, check $ x = 1, y = -1 $: $ k(0) = k(1) + k(-1) - 2k(-1) = 1 + k(-1) - 2k(-1) = 1 - k(-1) $. Also $ k(0) = k(0 + 0) = 2k(0) - 2k(0) = 0 $? No: $ k(0) = k(0 + 0) = 2k(0) - 2k(0) = 0 $. So $ k(0) = 0 $. Then $ 0 = 1 - k(-1) $ → $ k(-1) = 1 $. Then $ x = -1, y = -1 $: $ k(-2) = 2k(-1) - 2k(1) = 2(1) - 2(1) = 0 $. $ x = 1, y = -1 $: $ k(0) = k(1) + k(-1) - 2k(-1) = 1 + 1 - 2(1) = 0 $, consistent. Now $ x = 2, y = -1 $: $ k(1) = k(2) + k(-1) - 2k(-2) = 0 + 1 - 0 = 1 $, matches. No contradiction. Thus $ k(2) = 0 $. Final answer: $ oxed{0} $. 📰 Question: Find the remainder when $ x^5 - 3x^3 + 2x - 1 $ is divided by $ x^2 - 2x + 1 $. 📰 Solution: Note $ x^2 - 2x + 1 = (x - 1)^2 $. Use polynomial division or remainder theorem for repeated roots. Let $ f(x) = x^5 - 3x^3 + 2x - 1 $. The remainder $ R(x) $ has degree < 2, so $ R(x) = ax + b $. Since $ (x - 1)^2 $ divides $ f(x) - R(x) $, we have $ f(1) = R(1) $ and $ f'(1) = R'(1) $. Compute $ f(1) = 1 - 3 + 2 - 1 = -1 $. $ f'(x) = 5x^4 - 9x^2 + 2 $, so $ f'(1) = 5 - 9 + 2 = -2 $. $ R(x) = ax + b $, so $ R(1) = a + b = -1 $, $ R'(x) = a $, so $ a = -2 $. Then $ -2 + b = -1 $ → $ b = 1 $. Thus, remainder is $ -2x + 1 $. Final answer: $ oxed{-2x + 1} $.Question: A plant biologist is studying a genetic trait that appears in every 12th plant in a rows of crops planted in a 120-plant grid. If the trait is expressed only when the plant’s position number is relatively prime to 12, how many plants in the first 120 positions exhibit the trait? 📰 What 85 Centimeters Actually Spans In Inches No One Was Expecting This 8371061 📰 American Fd 689774 📰 Microsoft Teams Phone Mobile 8540930 📰 Roaring Fork Austin 7114064 📰 Step Up Your Church Atmosphere Shocking Church Outfits You Need To Try 963630 📰 Vietnam War Game Wiki 6720235 📰 How To Do Em Dash 5469785 📰 Best Decks Pokemon Tcg Pocket 2783713 📰 Secret Ship Parts Revealed Transform Your Boat Like A Pro Free Tips Inside 7378988 📰 Accesscorrectionscom Exclusive Guide To Erase Hidden Fees Reclaim Your Funds 1412867 📰 This Extreme Nfs Unbound Hack Split The Gaming Worldwatch What Happens Next 3055377 📰 Types Of German Shepherds 5156940 📰 Your Macbooks Tiny Keys Are Worn Beyond Repairfix It Before It Stops Working 2158954 📰 Films With Medusa 4575560 📰 The Ultimate Guide Convert Mp4 To Mov Like A Pro Free Tips Inside 2063543