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Write a linear factorization of the function.

f(x) = x4+ 9x2

f(x) = x2(x + 3i)(x - 3i)

f(x) = x2(x + 3i)2

f(x) = x2(3x + i)(3x - i)

f(x) = x2(3x + i)

Respuesta :

nobillionaireNobley
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:

[tex]f(x)=x^2(x+3i)(x-3i)[/tex]

Step-by-step explanation:

Given expression is,

[tex]f(x)=x^4+9x^2[/tex]

[tex]=x^2\{x^2+9\}[/tex]   ( Converse of distributive property )

[tex]=x^2\{x^2-i^2.9\}[/tex]    ( i² = -1 )

[tex]=x^2\{(x)^2-i^2(3)^2\}[/tex]

[tex]=x^2\{(x)^2-(3i)^2\}[/tex]

[tex]=x^2(x+3i)(x-3i)[/tex]      ( a² - b² = (a+b)(a-b) )

Since, further factorization is not possible,

Thus, the required linear factorization of the function is,

[tex]f(x)=x^2(x+3i)(x-3i)[/tex]

First option is correct.

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