Question

Write a linear factorization of the function. f(x) = x4 + 64x2

f(x) = x2(8x + i)(8x - i)
f(x) = x2(x + 8i)2
f(x) = x2(x + 8i)(x - 8i)
f(x) = x2(8x + i)2

Answer 1

We were given ;

f(x) = x⁴ + 64x²

x² is common to both terms so we factor it.

» f(x) = x²(x² + 64)

Now x² +64 has complex factors of (x+8i)(x-8i)

» f(x) = x²(x+8i)(x-8i)