Question

Write a linear factorization of the function. (2 points) f(x) = x4 + 36x2

Answer 1

f(x) = (x)(x)(x + 6i)(x - 6i)

Explanation:

Answer 2

The linear factorization is
`f(x)=(x)(x)(x+6i)(x-6i)`

Explanation:

we know that

A Linear Factorization is factored form of a polynomial in which each factor is a linear polynomial.

we have

`f(x)=x^(4)+36x^(2)`

step 1

Factor x^2

`x^(4)+36x^(2)=x^(2)[x^(2)+36]`

step 2

we know that

`x^(2)=(x)(x)`

substitute

`(x)(x)[x^(2)+36]`

step 3

Factor the sum of the squares

`[x^(2)+36]=(x+6i)(x-6i)`

substitute

`(x)(x)(x+6i)(x-6i)`

therefore

The linear factorization is
`f(x)=(x)(x)(x+6i)(x-6i)`