Matematyka

Proszę o pomoc, nikt nie wie jak to rozwalić. Muszę rozłożyć te wielomiany na czynniki.   A [latex]W(x) = x^{3}-4x+3[/latex]   B [latex]W(x) = x^{3} +2x^{2} -3 [/latex]   G [latex]W(x) = 2x^{4} -3x^{3} -2x^{2} + 3x [/latex] F [latex]W(x) = x^{5} - 3x^{4} -x^{3} +3x{2} -6x +18[/latex]


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W(x) = x³-4x+3 W(x) = x³-x-3x+3 W(x)= x(x²-1)-3(x-1) W(x)=x(x-1)(x+1)-3(x-1) W(x)= (x-1)[x(x+1)-3] W(x) = (x-1)(x²+x-3)   Δ=1-4*(-3) = 1+12=13   [latex]x_1=\frac{\sqrt{13}-1}{2}[/latex]   [latex]x_2=\frac{-\sqrt{13}-1}{2}[/latex]   [latex]W(x)=(x-1)(x-\frac{\sqrt{13}-1}{2})(x+\frac{\sqrt{13}+1}{2}) [/latex]   B) W(x) = x³  +2x² -3 W(x)= x³-1+2x² - 2 W(x) = (x-1)(x²+x+1)+2(x²-1) W(x) = (x-1)(x²+x+1)+2(x-1)(x+1) W(x) = (x-1)[x²+x+1+2(x+1)] W(x) = (x-1)(x²+x+1+2x+2) W(x) = (x-1)(x²+3x+3) Δ=9-12<0 więc zostawiamy tak jak jest, bo nie da się już 2 nawiasu rozpisać   G) W(x) = 2x⁴ -3x³ -2x² + 3x W(x) = 2x²(x²-1)-3x(x²-1) W(x)=(2x²-3x)(x²-1) W(x) = 2x(x-3)(x²-1) W(x) = 2x(x-3)(x-1)(x+1)   F) W(x) = x⁵ - 3x⁴ -x³ +3x² -6x +18 W(x) = x³(x²-1)-3x²(x²-1)-6(x-3) W(x) = (x²-1)(x³-3x²)-6(x-3) W(x)=(x-1)(x+1)*x²(x-3)-6(x-3) W(x)=(x-3)[(x-1)(x+1)x²-6] W(x) = (x-3)[(x²-1)x²-6] W(x)=(x-3)(x⁴-x²-6) teraz ropisujemy x⁴-x²-6 niech x²=t t²-t-6=0 Δ=1+24=25 t₁=(1+5)/2=3 t₂=(1-5)/2=-2   (t²-t-6)=(t-3)(t+2) x²=t (x²-3)(x²+2)=(x+√3)(x-√3)(x²+2)   W(x)=(x-3)(x-√3)(x+√3)(x²+2)  

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