Answer:
[tex]p(x)=-8(x+4)^2+128[/tex]
Step-by-step explanation:
Given, [tex]p(x)=-8x^2-64x[/tex]
Take -8 factor common,
[tex]p(x)=-8(x^2+8x)[/tex]
which can be written as
[tex]p(x)=-8(x^2+2 \times 4x)[/tex]
Add and subtract by 16 inside bracket,
[tex]p(x)=-8(x^2+2 \times 4x+16-16)[/tex]
[tex]p(x)=-8((x^2+2 \times 4x+4^2)-16)[/tex]
[tex]p(x)=-8((x+4)^2-16)[/tex]
[tex]p(x)=-8(x+4)^2+8 \times 16[/tex]
[tex]p(x)=-8(x+4)^2+128[/tex]
