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Sektion 1.5

[Matematik/Kalkulus (Lindstroem)/Kapitel 1]

Opgave 1

a) find P(x) : Q(x)
P(x) = 3x^{30 + 2x^{2} + 5x - 4, Q(x) = x - 3 3x^{3} + 2x^{2} + 5x - 4 : x - 3 = 3x^{2} + 11x + 38 3x^{3} - 9x^{2} 11x^{2} + 5x - 4 11x^{2} - 33x 38x - 4 38x - 114 110 P(x) : Q(x) = 3x^{2} + 11x + 38 + 110/(x - 3)

b) find P(x) : Q(x)
P(x) = x^{4} - 3x^{3} + 2x^{2} + 3x - 2, Q(x) = x^{2} + 2x - 1 x^{4} - 3x^{3} + 2x^{2} + 3x - 2 : x^{2} + 2x - 1 = x^{2} -5x + 13 x^{4} + 2x^{3} - x^{2} -5x^{3} + 3x^{2} + 3x - 2 -5x^{3} - 10x^{2} + 5x 13x^{2} - 2x - 2 13x^{2} + 26x - 13 -28x + 11 P(x) : Q(x) = x^{2} - 5x + 13 - (28x - 11)/(x^{2} + 2x - 1)

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