Question

Write a linear factorization of the function. f(x) = x4 + 81x2

Answer 1

f(x) = x2 (x + 9i)(x - 9i)

Answer 2

`f(x)= x^2(x+9i)(x-9i)`

Explanation:

`f(x) = x^4 + 81x^2`

Lets factor GCF x^2

`f(x) =x^2(x^2+81)`

Now factor out
`x^2+81`

LEts find out factors by solving, set the parenthesis =0 and solve for x

`x^2+81=0`

Subtract 81 on both sides

`x^2=-81`

take square root on both sides

`x^2=√(-81)`

`√(-1) =i`

`x=i√(81)`

`x=+-9i`

Two roots are
`x=-9i , x=+9i`

Factors are
`(x+9i)(x-9i)`

So
`f(x)= x^2(x+9i)(x-9i)`