a,\(x^2-4x-5=0\)

\(\Rightarrow x^2-x+5x-5=0\)

\(\Rightarrow x\left(x-1\right)+5\left(x-1\right)=0\)

\(\Rightarrow\left(x-1\right)\left(x+5\right)=0\Rightarrow\left[{}\begin{matrix}x-1=0\\x+5=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=1\\x=-5\end{matrix}\right.\)

b, \(2x^2-6x+4=0\)

\(\Rightarrow2x^2-2x-4x+4=0\)

\(\Rightarrow2x\left(x-1\right)-4\left(x-1\right)=0\)

\(\Rightarrow\left(x-1\right)\left(2x-4\right)=0\Rightarrow\left[{}\begin{matrix}x-1=0\\2x-4=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

c, \(5x^2-x-18=0\)

\(\Rightarrow5x^2-10x+9x-18=0\)

\(\Rightarrow5x\left(x-2\right)+9\left(x-2\right)=0\)

\(\Rightarrow\left(x-2\right)\left(5x+9\right)=0\Rightarrow\left[{}\begin{matrix}x-2=0\\5x+9=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{9}{5}\end{matrix}\right.\)

d, \(2x^3-3x^2+x+30\)

(bạn xem lại đề nha)

e, \(5x^3-21x^2+11x+5\)

\(=5x^3-5x^2-16x^2+16x-5x+5\)

\(=5x^2\left(x-1\right)-16x\left(x-1\right)-5\left(x-1\right)\)

\(=\left(x-1\right)\left(5x^2-16x-5\right)\)

Chúc bạn học tốt!!!

Giải phương trình: (2x - 5)3 - (x - 2)3 = (x - 3)3

\(\left(2x-5\right)^3-\left(x-2\right)^3=\left(x-3\right)^3\)

\(\Leftrightarrow\left(2x-5-x+2\right)\left(4x^2-20x+25+2x^2-9x+10+x^2-4x+4\right)=\left(x-3\right)^3\)

\(\Leftrightarrow\left(x-3\right)\left(7x^2-33x+39\right)-\left(x-3\right)^3=0\)

\(\Leftrightarrow\left(x-3\right)\left(7x^2-33x+39-x^2+6x-9\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(6x^2-27x+30\right)=0\)

\(\Leftrightarrow\left(x-3\right)3\left(2x^2-9x+10\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(2x^2-4x-5x+10\right)=0\)

\(\Leftrightarrow\left(x-3\right)[2x\left(x-2\right)-5\left(x-2\right)]=0\)

\(\Leftrightarrow\left(x-3\right)\left(x-2\right)\left(2x-5\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-3=0\\x-2=0\\2x-5=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=3\\x=2\\x=\dfrac{5}{2}\end{matrix}\right.\)

\(S=\left\{2;\dfrac{5}{2};3\right\}\)