Answer:
[tex](64x^2+80x+25)[/tex]
Step-by-step explanation:
The polynomial [tex]512x^3-125[/tex] has the form of a difference of cubes [tex](a^3-b^3)[/tex]. This form factors into [tex](a-b)(a^2+2ab+b^2)[/tex].
512 is the cube of 8 so a=8. 125 is the cube 5 so b=5.
It factors as [tex](a-b)(a^2+2ab+b^2)= (8x-5)(64x^2+80x+25)[/tex].
