Rozłóż wielomian w na czynniki: a)  w(x)= x^4 - 7x^3     b) w(x)= 18x^3 + 30x^2                                                 c) w(x)= -2x^5 - 8x^4    d) w(x)= x^3 - 25x     Dam NAJ :)

a) [latex] w(x)= x^{4}-7x^{3}=x^{3}(x-7)[/latex] b) [latex]w(x)= 18x^{3} + 30x^{2}=6x^{2}(3x+5)[/latex] c) [latex] w(x)= -2x^{5} - 8x^{4}=-2x^{4}(x+4)[/latex] d) Korzystamy ze wzoru skróconego mnożenia: [latex]a^{2}-b^{2}=(a-b)(a+b)\\w(x)= x^{3} - 25x=x(x^{2}-25)=x(x-5)(x+5)[/latex]

[latex]a)\ wx =x^4 - 7x^3 =x^{3}(x-1)\ \b)\ w(x)= 18x^3 + 30x^2=6x^{2}(3x+5)\ \c)\w(x)= -2x^5 - 8x^4 =-2x^{4}(x+4)\ \d)\ w(x)= x^3 - 25x =x(x^{2}-25) =x(x-5)(x+5)[/latex]