Question

Sprowadź do postaci iloczynowej następujące wielomiany:

a). y=-2x-3

b). y=9+6x+1

c). y=-2(x+3)+8

Answer 1

a)

y = x^2 - 2x - 3

delta = 4 -4*1*(-3) = 4 + 12 = 16

x1 = [2 -4]/2 = -2/2 = -1

x2 = [2 + 4]/2 = 6/2 = 3

Ponieważ a = 1

zatem

y = (x +1)*(x - 3)

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b)

y = 9x^2 + 6x + 1

y = (3x + 1)^2  = (3x +1)*(3x +1) = 3*(x + 1/3)*3*(x + 1/3)

y = 9*(x +1/3)*(x + 1/3)

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c)

y = -2(x +3)^2 + 8

y = -2(x^2 +6x + 9) + 8 = -2 x^2 - 12x - 18 + 8 = -2x^2 - 12x - 10

delta = 144 - 4*(-2)*(-10) = 144 - 80 = 64

x1 = [ 12 - 8]/(-4) = 4/(-4) = -1

x2 = [ 12 + 8]/(-4) = 20/(-4) = - 5

Ponieważ a = -2 zatem

y = -2*(x +1)*(x + 5)

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Korzystaliśmy z wzoru

a x^2 + bx + c = a(x -x1)*(x - x2)

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