Answer:
[tex]x(x+2)(x-5)[/tex]
Step-by-step explanation:
First, note that x is the common factor, then
[tex]x^3-3x^2-10x=x(x^2-3x-10).[/tex]
Now find the discriminant of the quadratic polynomial [tex]x^2-3x-10:[/tex]
[tex]D=(-3)^2-4\cdot (-10)=9+40=49.[/tex]
Thus,
[tex]x_1=\dfrac{-(-3)-\sqrt{49}}{2}=\dfrac{3-7}{2}=-2,\\ \\x_2=\dfrac{-(-3)+\sqrt{49}}{2}=\dfrac{3+7}{2}=5.[/tex]
Hence,
[tex]x^3-3x^2-10x=x(x^2-3x-10)=x(x+2)(x-5).[/tex]
