Question

Which method is best to factor f(x) = x^2 - 81?

Answer 1

use difference of 2 perfect squares

remember that $a^2-b^2=(a-b)(a+b)$

so
$x^2-81=$
$x^2-9^2=$
$(x-9)(x+9)$
there, factored

Answer 2

Use the difference of perfect squares

f(x) = x^2 - 81

f^2 - 81 = (f x -9), (f x 9)

f(f) = f^2 , f(-9) = -9f , f(9) = 9f , -9(9) = -81

(f(-9)), (f(9)) is your factors

hope this helps