Rozłóż wielomian na czynniki pierwsze : A. 9x^3-9x^2+4x-4 [latex]9 x^{3} - 9x^{2} + 4x - 4 = 9 x^{2} (x - 1) + 4(x-1) = (x-1)(9 x^{2} + 4) [/latex] B. -6x^4+8x^3-3x^2+4x [latex]-6 x^{4} + 8 x^{3} - 3 x^{2} + 4x = -2 x^{3}(3x-4) + x(3x-4) = \ = (3x-4)(x - 2 x^{3}) [/latex] c. 5x^5+2x^4+10x^3+4x^2 [latex]5x^{5} + 2x^{4} + 10x^{3} + 4x^{2} = x^{4}(5x+2) + 2x^{2}((5x+2)) = \ = (5x+2)(x^{4}+ 2x^{2}) = (5x + 2)(x^{2} + 2) x^{2} [/latex] D. -4x^4+5x^3+12x-15 [latex]-4 x^{4} + 5 x^{3} + 12x - 15 = - x^{3}(4x+5) + 3((4x+5) = \ = (4x+5)(-x^{3} + 3) [/latex] rozwiąż równanie A. -2x^2 +x+1=0 [latex]-2x^{2} + x + 1 = 0 [/latex] Δ = 1 - 4*(-2)*1 Δ = 1 + 8 Δ = 9 √Δ = 3 [latex] x_{1} = frac{-1 - 3}{-4} \ x_{1} = frac{-4}{-4} \ x_{1} = 1 \ x_{2} = frac{-1 + 3}{-4} \ x_{2} = -frac{1}{2} [/latex] b. 5x^2-2x=-3 [latex]5 x^{2} - 2x = -3 \ 5 x^{2} - 2x + 3 = 0[/latex] Δ < 0 x ∈ Ф C. 9x2=3x+2 [latex] 9x^{2} - 3x - 2 = 0[/latex] Δ = 9 + 72 Δ = 81 Δ = 9 [latex] x_{1} = frac{3 - 9}{18} \ x_{1} = frac{-6}{18} \ x_{1} = - frac{1}{3} \ x_{2} = frac{9}{18} \ x_{2} = frac{1}{2} [/latex] D. 3x^2-5x=x^2+2x-3 [latex]3 x^{2} - 5x - x^{2} - 2x + 3 = 0 \ 2 x^{2} - 3x + 3 = 0[/latex] Δ < 0
