rozłóż wielomian na czynniki:
a) w(x) = x^3 - x^2 + x - 1
b) w(x) = x^3 - 2x^2 - 2x + 4
c) w(x) = 2x^3 -3x^2 +4x - 6
a) w(x) = x^3 - x^2 + x - 1 = x²(x-1)+(x-1) = (x²+1)(x-1)
b) w(x) = x^3 - 2x^2 - 2x + 4 = x²(x-2)-2(x-2) = (x²-2)(x-2) = (x-√2)(x+√2)(x-2)
c) w(x) = 2x^3 -3x^2 +4x - 6 = x²(2x-3)+2(2x-3) = (x²+2)(2x-3)
a)
w(x)=x^2(x-1)+1(x-1)=(x-1)(2+1)=3(x-1)
b)
w(x) = x^3 - 2x^2 - 2x + 4= x^2( x- 2)-2(x-2)=(x-2)(x^2 -2)
c)
w(x) = 2x^3 -3x^2 +4x - 6= x^2 ( 2x- 3) +2 (2x-3)= (2x-3)(x^2+2)
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a) w(x) = x^3 - x^2 + x - 1 = x²(x-1)+(x-1) = (x²+1)(x-1)
b) w(x) = x^3 - 2x^2 - 2x + 4 = x²(x-2)-2(x-2) = (x²-2)(x-2) = (x-√2)(x+√2)(x-2)
c) w(x) = 2x^3 -3x^2 +4x - 6 = x²(2x-3)+2(2x-3) = (x²+2)(2x-3)
a)
w(x)=x^2(x-1)+1(x-1)=(x-1)(2+1)=3(x-1)
b)
w(x) = x^3 - 2x^2 - 2x + 4= x^2( x- 2)-2(x-2)=(x-2)(x^2 -2)
c)
w(x) = 2x^3 -3x^2 +4x - 6= x^2 ( 2x- 3) +2 (2x-3)= (2x-3)(x^2+2)