Question

Write a linear factorization of the function. f(x) = x4 + 49x2

Answer 1

102 i thinks its the answer

Answer 2

f(x) =
`x^2 (x + 7i)(x  - 7i)`

Explanation:

The given function is f(x) =
`x^4 + 49x^2`

Here x^2 is a common factor, so we take out and write the remaining term inside the parenthesis.

f(x) =
`x^2 (x^2 + 49)`

f(x) =
`x^2 (x^2 - (7i)^2)` [Here i^2 = -1]

We know that a^2 - b^2 = (a +b)(a-b) using this identity, we get

f(x) =
`x^2 (x + 7i)(x - 7i)`