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.
