Question

Write a linear factorization of the function. (5 points) f(x) = x4 + 81x2

Answer 1

F(x) = x^4 + 81x^2
f(x) = x^2*x^2 + x^2*81
f(x) = x^2*(x^2 + 81) ... see note 1
f(x) = x^2*(x + 9i)(x - 9i) ... see note 2

note 1: if you haven't learned about complex or imaginary numbers yet, then you would stop at the line with "note 1" on it

note 2: you would stop here if you have learned about complex or imaginary numbers and you want to factor over the complex numbers. I used the rule that
a^2 + b^2 = (a+bi)*(a-bi)