Answer:
The linear factorization is [tex]f(x)=(x)(x)(x+6i)(x-6i)[/tex]
Step-by-step explanation:
we know that
A Linear Factorization is factored form of a polynomial in which each factor is a linear polynomial.
we have
[tex]f(x)=x^{4}+36x^{2}[/tex]
step 1
Factor x^2
[tex]x^{4}+36x^{2}=x^{2}[x^{2}+36][/tex]
step 2
we know that
[tex]x^{2}=(x)(x)[/tex]
substitute
[tex](x)(x)[x^{2}+36][/tex]
step 3
Factor the sum of the squares
[tex][x^{2}+36]=(x+6i)(x-6i)[/tex]
substitute
[tex](x)(x)(x+6i)(x-6i)[/tex]
therefore
The linear factorization is [tex]f(x)=(x)(x)(x+6i)(x-6i)[/tex]
