1.
[tex](4-x)(x^{2}+2x-15) = 0\\\\(4-x)(x^{2}-3x+5x-15) = 0\\\\(4-x)[x(x-3)+5(x-3)] = 0\\\\(4-x)(x-3)(x+5) = 0\\\\4-x = 0 \ \vee \ x-3 =0 \ \vee \ x+5 = 0\\\\x = 4 \ \vee \ x = 3 \ \vee \ x = -5\\\\x -\n \{-5, 3, 4\}\\[/tex]
2.
[tex]x^{3}-7x^{2}-4x+28 = 0\\\\x^{2}(x-7) - 4(x-7) = 0\\\\(x-7)(x^{2}-4) = 0\\\\(x-7)(x-2)(x+2) = 0\\\\x-7 = 0 \ \vee \ x-2 \ \vee \ x+2 = 0\\\\x = 7 \ \vee \ x = 2 \ \vee \ x = -2\\\\x \in \{-2, 2, 7\}[/tex]
3.
a)
Sprawdzamy, czy W(1) = 30
[tex]W(x) = x^{3}-5x^{2}-9x+45\\\\W(1) = 1-5-9+45 = 32 \neq 30[/tex]
Punkt A=(1, 30) nie należy do wykresu tego wielomianu.
b)
[tex]x^{3}-5x^{2}-9x+45 = x^{2}(x-5) - 9(x-5) = (x-5)(x^{2}-9) = (x-5)(x-3)(x+3)[/tex]
