Forumet - Matte C hjälp

Matte C hjälp

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p(x) = x^2 - 10x + 16


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Uppgift:

Faktorisera polynomet p(x) = x²-10x+16

Lösning:

p(x) = x²-10x+16
p(x) = 0
x²-10x+16 = 0
x = (-1/2)(-10)±√(((-1/2)(-10))²-16)
x = 1*10/2±√((1*10/2)²-16)
x = 10/2±√((10/2)²-16)
x = 5±√(5²-16)
x = 5±√(25-16)
x = 5±√9
x = 5±3
x = 5-3 eller x = 5+3
x = 2 eller x = 8
x²-10x+16 = (x-2)(x-8)
p(x) = (x-2)(x-8)

Kontroll:

(x-2)(x-8) = (x+(-2))(x+(-8))
(x-2)(x-8) = xx+x(-8)+(-2)x+(-2)(-8)
(x-2)(x-8) = x²+(-8x)+(-2x)+16
(x-2)(x-8) = x²-8x-2x+16
(x-2)(x-8) = x²-10x+16
x²-10x+16 = (x-2)(x-8)
p(x) = (x-2)(x-8)

Resultat:

p(x) = (x-2)(x-8)

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