Question

x3 – 5x2 – x + 5 = 0

Answer 1

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

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

Answer 2

\(\Leftrightarrow x^2\left(x-5\right)-\left(x-5\right)=0\\ \Leftrightarrow\left(x^2-1\right)\left(x-5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-1\\x=1\\x=5\end{matrix}\right.\)

Answer 3

\(x^3-5x^2-x+5=x^2\left(x-5\right)-\left(x-5\right)=\left(x-5\right)\left(x^2-1\right)=\left(x-5\right)\left(x-1\right)\left(x+1\right)\)