Question

Write a linear factorization of the function.

Answer 1

F(x) = x^4 + 9x^2 = x^2(x^2 + 9) = x^2(x^2 - (-9)) = x^2(x - sqrt(-9))(x + sqrt(-9)) = x^2(x + 3i)(x - 3i)

Answer 2

Answer:

$f(x)=x^2(x+3i)(x-3i)$

Step-by-step explanation:

Given expression is,

$f(x)=x^4+9x^2$

$=x^2\{x^2+9\}$   ( Converse of distributive property )

$=x^2\{x^2-i^2.9\}$    ( i² = -1 )

$=x^2\{(x)^2-i^2(3)^2\}$

$=x^2\{(x)^2-(3i)^2\}$

$=x^2(x+3i)(x-3i)$      ( a² - b² = (a+b)(a-b) )

Since, further factorization is not possible,

Thus, the required linear factorization of the function is,

$f(x)=x^2(x+3i)(x-3i)$

First option is correct.