The given function is:
[tex]f(x)=x^4-25x^2+144[/tex]
Split 25 into two using factors of 144 (-16 and -9):
[tex]x^4-16x^2-9x^2+144[/tex]
Factorize each pair of expressions:
[tex]\begin{gathered} x^2(x^2-16)-9(x^2-16) \\ =(x^2-16)(x^2-9) \end{gathered}[/tex]
Factorize further using the difference of two squares:
[tex]\begin{gathered} (x^2-4^2)(x^2-3^2) \\ =(x-4)(x+4)(x-3)(x+3) \end{gathered}[/tex]
Hence, the factored form of the function is:
[tex]f(x)=(x-4)(x+4)(x-3)(x+3)[/tex]
