Question

Write a linear factorization of the function.

Answer 1

Answer:

  f(x) = x^2 (x + 7i)(x - 7i)

Step-by-step explanation:

Factoring out x^2 gives ...

  f(x) = x^2(x^2 +49)

The factor with 49 can be considered to be the difference of two squares, where one of the squares is -49. Then its square root is ±7i, and the factorization of that term is ...

  x^2 +49 = (x +7i)(x -7i)

So, the overall factorization of f(x) is ...

  f(x) = x^2(x +7i)(x -7i)