Lösung:
Anmerkung: W(3) bedeutet Quadratwurzel aus 3
zu a) x³ + 5x² - 9x - 45 = x²(x + 5) - 9(x + 5) = (x² - 9)(x + 5) = (x - 3)(x + 3)(x + 5)
zu b) x³ - 9x² + 5x - 45 = x²(x - 9) + 5(x - 9) = (x² + 5)(x - 9)
zu c) 2x³ + 10x² - 12x - 60 = 2x²(x - 5) - 12(x - 5) = 2(x² - 6)(x - 5) = 2(x - W(6))(x + W(6))(x - 5)
zu d) 6x4 - 15x² - 54 = 6x4 + 12x² - 27x² - 54 = 6x²(x² + 2) - 27(x² + 2) = 6(x² - 4,5)(x² + 2)
= 6(x - W(4,5))(x + W(4,5))(x² + 2)
zu e) x5 - 5x³ - 24x = x5 + 3x³ - 8x³ - 24x = x³(x² + 3) - 8x(x² + 3) = x(x² - 8)(x² + 3)
= x(x - 2W(2))(x + 2W(2))(x² + 3)
zu f) x4 - 8x² + 16 = (x² - 4)² = (x - 2)²(x + 2)²
zu g) 10x4 - 20x² + 10 = 10(x4 - 2x² + 1) = 10(x²- 1)² = 10(x - 1)²(x + 1)²
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