zad 1. Rozłóż wielomiany na czynniki: a) x3+ 6x2 - 3x - 18 b) 25x2 - 7 c) 3x3 + 2x2 - x d) x2 - 5x + 6 e) x3 + 27 f) x2 - 2xy + y2 - 4
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a) x³+6x²-3x-18=(x³-3x)+(6x²-18)=x(x²-3)+6(x²-3)=(x²-3)(x+6)
c) 3x³+2x²-x=3x³-1x²+3x²-x=(3x²+3x²)+(-1x²-x)=3x²(x+1)-x(x+1)=(3x²-x)(x+1)
d) x²-5x+6=0
Δ=(-5)²-4*1*6
Δ=1
x1=6/2=3
x2=4/2=2
e) x³+27=x³+3³=(x+3)(x²-3x+9)