Find the LCM of the given polynomials. \( x^{3}-64 x ; x^{3}-16 x^{2}+64 x \) and \( x^{3}-512 \) The LCM is \( \square \). (Factor completely.)

В) \( \log _{5}^{2}(2 x)-20 \log _{5}(2 x)=21 \).

Factor \( f(x)=2 x^{3}+9 x^{2}-51 x+40 \) into linear factors given that -8 is a zero of \( f(x) \). \( f(x)=2 x^{3}+9 x^{2}-51 x+40=\square \) \( ( \) Factor completely.)

Determina per quare valore di a la funzlone \( y=\frac{x}{a-x} \) ha dominio \( D: x \neq-2 \). \( P(2 ; 5) \). \[ [a=8, b=2 \mid \]

Divide the expression. \( \frac{3 x^{4}-7 x^{3}+6 x-18}{3 x-7} \) \( \frac{3 x^{4}-7 x^{3}+6 x-18}{3 x}=\square \) (Simplify your answer.)

Divide the expression. \( \frac{6 x^{4}-2 x^{2}+6}{x^{2}+2} \) \( \frac{6 x^{4}-2 x^{2}+6}{x^{2}+2}=\square \) (Simplify your answer.)