miniaufgabe.js ==== 23. September 2019 bis 27. September 2019 ==== === Dienstag 24. September 2019 === Der **TR (Ti-Nspire)** ist dabei und aufgeladen. Sonst keine weitere Miniaufgabe. Der Server hat sich am Montag Morgen 4:02 überhitzt und abgeschaltet. Ich konnte den Server erst um 22:00 wieder hochfahren, vorher konnte ich leider nicht an die Schule kommen (und der technische Support hat (noch) nicht geantwortet). === Donnerstag 26. September 2019 === Der **TR (Ti-Nspire)** ist dabei und aufgeladen. Ausmultiplizeren, Zusammenfassen, FaktorisierenminiAufgabe("#exoausmult_faktor","#solausmult_faktor", [["$-\\frac{5}{8}x^2 -\\frac{35}{16}x -\\frac{15}{8} + \\left(\\frac{1}{2}x +\\frac{3}{4}\\right)\\cdot\\left(-\\frac{3}{4}x -\\frac{1}{2}\\right)$", "$-\\frac{5}{8}x^2 -\\frac{35}{16}x -\\frac{15}{8} -\\frac{3}{8}x^2 -\\frac{13}{16}x -\\frac{3}{8} = -1x^2 -3x -\\frac{9}{4} = -\\frac{1}{4}\\cdot\\left(4x^2+12x+9\\right) = -\\frac{1}{4}\\cdot\\left(2x + 3\\right)^2$"], ["$\\frac{25}{8}x^2 +\\frac{85}{12}x +\\frac{14}{3} + \\left(-\\frac{3}{4}x -\\frac{1}{2}\\right)\\cdot\\left(\\frac{1}{6}x -\\frac{4}{3}\\right)$", "$\\frac{25}{8}x^2 +\\frac{85}{12}x +\\frac{14}{3} -\\frac{1}{8}x^2 +\\frac{11}{12}x +\\frac{2}{3} = 3x^2 +8x +\\frac{16}{3} = \\frac{1}{3}\\cdot\\left(9x^2+24x+16\\right) = \\frac{1}{3}\\cdot\\left(3x + 4\\right)^2$"], ["$\\frac{17}{40}x^2 +\\frac{25}{8}x +\\frac{8}{5} + \\left(\\frac{1}{2}x -\\frac{4}{5}\\right)\\cdot\\left(\\frac{3}{4}x -\\frac{1}{4}\\right)$", "$\\frac{17}{40}x^2 +\\frac{25}{8}x +\\frac{8}{5} +\\frac{3}{8}x^2 -\\frac{29}{40}x +\\frac{1}{5} = \\frac{4}{5}x^2 +\\frac{12}{5}x +\\frac{9}{5} = \\frac{1}{5}\\cdot\\left(4x^2+12x+9\\right) = \\frac{1}{5}\\cdot\\left(2x + 3\\right)^2$"], ["$-1x^2 -\\frac{83}{40}x -\\frac{77}{40} + \\left(-\\frac{4}{5}x +\\frac{1}{2}\\right)\\cdot\\left(-\\frac{1}{4}x +\\frac{1}{4}\\right)$", "$-1x^2 -\\frac{83}{40}x -\\frac{77}{40} +\\frac{1}{5}x^2 -\\frac{13}{40}x +\\frac{1}{8} = -\\frac{4}{5}x^2 -\\frac{12}{5}x -\\frac{9}{5} = -\\frac{1}{5}\\cdot\\left(4x^2+12x+9\\right) = -\\frac{1}{5}\\cdot\\left(2x + 3\\right)^2$"], ["$-\\frac{53}{15}x^2 -\\frac{24}{5}x -\\frac{22}{15} + \\left(-\\frac{1}{2}x -\\frac{1}{2}\\right)\\cdot\\left(-\\frac{2}{3}x +\\frac{2}{3}\\right)$", "$-\\frac{53}{15}x^2 -\\frac{24}{5}x -\\frac{22}{15} +\\frac{1}{3}x^2 +0x -\\frac{1}{3} = -\\frac{16}{5}x^2 -\\frac{24}{5}x -\\frac{9}{5} = -\\frac{1}{5}\\cdot\\left(16x^2+24x+9\\right) = -\\frac{1}{5}\\cdot\\left(4x + 3\\right)^2$"], ["$-\\frac{59}{14}x^2 -\\frac{31}{6}x -\\frac{11}{7} + \\left(-\\frac{2}{3}x -\\frac{3}{2}\\right)\\cdot\\left(\\frac{3}{7}x +\\frac{2}{7}\\right)$", "$-\\frac{59}{14}x^2 -\\frac{31}{6}x -\\frac{11}{7} -\\frac{2}{7}x^2 -\\frac{5}{6}x -\\frac{3}{7} = -\\frac{9}{2}x^2 -6x -2 = -\\frac{1}{2}\\cdot\\left(9x^2+12x+4\\right) = -\\frac{1}{2}\\cdot\\left(3x + 2\\right)^2$"], ["$\\frac{19}{10}x^2 +\\frac{23}{5}x +\\frac{33}{10} + \\left(-\\frac{1}{2}x +\\frac{1}{2}\\right)\\cdot\\left(\\frac{1}{5}x -\\frac{1}{5}\\right)$", "$\\frac{19}{10}x^2 +\\frac{23}{5}x +\\frac{33}{10} -\\frac{1}{10}x^2 +\\frac{1}{5}x -\\frac{1}{10} = \\frac{9}{5}x^2 +\\frac{24}{5}x +\\frac{16}{5} = \\frac{1}{5}\\cdot\\left(9x^2+24x+16\\right) = \\frac{1}{5}\\cdot\\left(3x + 4\\right)^2$"], ["$-3x^2 -\\frac{41}{7}x -\\frac{51}{14} + \\left(\\frac{3}{2}x -\\frac{3}{2}\\right)\\cdot\\left(\\frac{2}{3}x +\\frac{4}{7}\\right)$", "$-3x^2 -\\frac{41}{7}x -\\frac{51}{14} +1x^2 -\\frac{1}{7}x -\\frac{6}{7} = -2x^2 -6x -\\frac{9}{2} = -\\frac{1}{2}\\cdot\\left(4x^2+12x+9\\right) = -\\frac{1}{2}\\cdot\\left(2x + 3\\right)^2$"], ["$\\frac{9}{5}x^2 +\\frac{91}{60}x +\\frac{7}{9} + \\left(\\frac{1}{2}x -\\frac{2}{3}\\right)\\cdot\\left(-\\frac{3}{5}x +\\frac{1}{6}\\right)$", "$\\frac{9}{5}x^2 +\\frac{91}{60}x +\\frac{7}{9} -\\frac{3}{10}x^2 +\\frac{29}{60}x -\\frac{1}{9} = \\frac{3}{2}x^2 +2x +\\frac{2}{3} = \\frac{1}{6}\\cdot\\left(9x^2+12x+4\\right) = \\frac{1}{6}\\cdot\\left(3x + 2\\right)^2$"], ["$-\\frac{5}{6}x^2 -\\frac{67}{40}x -\\frac{33}{20} + \\left(-\\frac{1}{3}x +\\frac{1}{4}\\right)\\cdot\\left(-\\frac{1}{2}x +\\frac{3}{5}\\right)$", "$-\\frac{5}{6}x^2 -\\frac{67}{40}x -\\frac{33}{20} +\\frac{1}{6}x^2 -\\frac{13}{40}x +\\frac{3}{20} = -\\frac{2}{3}x^2 -2x -\\frac{3}{2} = -\\frac{1}{6}\\cdot\\left(4x^2+12x+9\\right) = -\\frac{1}{6}\\cdot\\left(2x + 3\\right)^2$"]], "
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