Answered

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1 Factor each polynomial over the set of realC)f(x) = x^4- 25x^2 + 144

Sagot :

Notice that:

[tex]\begin{gathered} x^4-25x^2+144=(x^2)^2+(-9-16)x^2+(-9)(-16) \\ =(x^2-9)(x^2-16)\text{.} \end{gathered}[/tex]

Now, notice that:

[tex]\begin{gathered} x^2-9=x^2-3^2=(x+3)(x-3), \\ x^2-16=x^2-4^2=(x+4)(x-4)\text{.} \end{gathered}[/tex]

Therefore:

[tex]x^4-25x^2+144=(x+3)(x-3)(x+4)(x-4)\text{.}[/tex]

Answer:

[tex]x^4-25x^2+144=(x+3)(x-3)(x+4)(x-4)\text{.}[/tex]

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