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📰 Solution: Let $ u = \sqrt{x} $, so $ u \geq 0 $. Substituting, the equation becomes $ u + 3u^2 = 4 $. Rearranging: $ 3u^2 + u - 4 = 0 $. Using the quadratic formula: $ u = \frac{-1 \pm \sqrt{1 + 48}}{6} = \frac{-1 \pm 7}{6} $. Valid solution: $ u = 1 $ (since $ u \geq 0 $). Thus, $ \sqrt{x} = 1 \Rightarrow x = 1 $. \boxed{1} 📰 Question: Find the remainder when $ x^5 - 2x^3 + x^2 + 1 $ is divided by $ x^2 - 3x + 2 $, focusing on polynomial division techniques. 📰 Solution: Factor the divisor: $ x^2 - 3x + 2 = (x-1)(x-2) $. Use the Remainder Theorem: Let $ R(x) = ax + b $ be the remainder. Evaluate $ f(1) = 1 - 2 + 1 + 1 = 1 = a(1) + b $. Evaluate $ f(2) = 32 - 16 + 4 + 1 = 21 = a(2) + b $. Solve: $ a + b = 1 $, $ 2a + b = 21 $. Subtract: $ a = 20 $, then $ b = -19 $. Remainder: $ 20x - 19 $. \boxed{20x - 19} 📰 Limitless Access Just Enter This Command To Open Control Panel Now 9798984 📰 How The U Wii U Outperforms The U Puppyexplosive Features You Need To Try 6244919 📰 Watch The Jackal 8882785 📰 Banks That Are Open 9765657 📰 President Of Korea 4068476 📰 Rodimus 7469442 📰 Wait Maybe The Sum Is 440 But Its Not Asked For N But The Number No What Is The Largest Integer 2716031 📰 The Ultimate Bart Simpson Clipyou Need To See This Fan Obsession Now 9227062 📰 Apple Scroll Bar 3663643 📰 Camper Water Filter 9192598 📰 Why Gamers Are Rcing Over Game Aqyou Must Watch This 4304634 📰 Life 1999 Why This Decade Still Shapes Our Present The Complete Journey 8028071 📰 Atlanta Tech College 2963692 📰 Volition Meaning 2031053 📰 Cleveland America 4045425