Question

Factor each polynomial already set a real numbers. Question (C)

Answer 1

The given function is:

`f(x)=x^4-25x^2+144`

Split 25 into two using factors of 144 (-16 and -9):

`x^4-16x^2-9x^2+144`

Factorize each pair of expressions:

`\begin{gathered} x^2(x^2-16)-9(x^2-16) \\ =(x^2-16)(x^2-9) \end{gathered}`

Factorize further using the difference of two squares:

`\begin{gathered} (x^2-4^2)(x^2-3^2) \\ =(x-4)(x+4)(x-3)(x+3) \end{gathered}`

Hence, the factored form of the function is:

`f(x)=(x-4)(x+4)(x-3)(x+3)`