Answer:
C. [tex](4x-8)^2[/tex]
Step-by-step explanation:
We need to determine whether the given polynomial [tex]16x^2-64x+64[/tex] can be factored into perfect squares. If so, factor the polynomial. Otherwise, select that it cannot be factored into a perfect square.
[tex]16x^2-64x+64[/tex]
[tex]=16x^2-32x-32x+64[/tex]
[tex]=16x(x-2)-32(x-2)[/tex]
[tex]=(16x-32)(x-2)[/tex]
[tex]=16(x-2)(x-2)[/tex]
[tex]=16(x-2)^2[/tex]
[tex]=4^2(x-2)^2[/tex]
[tex]=(4(x-2))^2[/tex]
[tex]=(4x-8)^2[/tex]
Hence final answe is choic C. [tex](4x-8)^2[/tex]
