Rozłóż wielomian na czynniki a) w(x)=2x³+2x²-12x = 2x(x²+x-6) z nawiasu liczymy Δ=b²-4ac = 1²+4*1*6=1+24=25 √Δ=5 x1 =(-b-√Δ)/2a = -1-5/2*1=-6/2=-3 x2=(-b+√Δ)/2a = -1+5/2*1 = 4/2=2 w(x)=2x(x+3)(x-4) b) w(x)=7x³+2x²+x = x(7x²+2x+1) z nawiasu liczymy Δ=b²-4ac = 4²-4*1*7 = 16-28 = -12 Δ jest ujemna wiec nie da sie rozłozyc nawiasu czyli wynik zostaje jak wyzej c) w(x)=x³-5x²-25x+125 = x²(x-5)-25(x+5)= (x-5)(x+5)(x-5) d) w(x)=x³-3x²-4x+12 =x²(x-3)-4(x+3)=(x-2)(x-3)(x+3) e) w(x)=7x⁸-21x⁶= 7x^6(x²-3)=7x^6(x+√3)(x-√3) f) w(x)=-3x³+27x²=-3x² (x+9) g) w(x)=x³-3x²-x+3= x²(x-3)-(x-3) h) w(x)=4x³+4x²-25x-25=4x²(x+1)-25(x+1)
a) w(x)=2x³+2x²-12x W(x)=2x(x²+x-6) Δ=1-4*(-6)=1+24=25 √Δ=5 x₁=(-1-5)/2=-6/2=-3 x₂=(-1+5)/2=4/2=2 W(x)=2x(x-2)(x+3) b) w(x)=7x³+2x²+x W(x)=x(7x²+2x+1) Δ=4-4*7=4-28<0 c) w(x)=x³-5x²-25x+125 W(x)=x²(x-5)-25(x-5) W(x)=(x-5)(x²-25) W(x)=(x-5)(x-5)(x+5) d) w(x)=x³-3x²-4x+12 W(x)=x²(x-3)-4(x-3) W(x)=(x-3)(x²-4) W(x)=(x-3)(x-2)(x+2) e) w(x)=7x⁸-21x⁶ W(x)=7x⁶(x²-3) W(x)=7x⁶(x-√3)(x+√3) f) w(x)=-3x³+27x² W(x)=-3x²(x-9) g) w(x)=x³-3x²-x+3 W(x)=x²(x-3)-(x-3) W(x)=(x-3)(x²-1) W(x)=(x-3)(x-1)(x+1) h) w(x)=4x³+4x²-25x-25 W(x)=4x²(x+1)-25(x+1) W(x)=(x+1)(4x²-25) W(x)=(x+1)(2x-5)(2x+5)
