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Hello guys,

I'd like to ask you how to efficiently factorize complicated polynomial like this one for example:

$$\frac{128t^4+128t^3+192t^2+32t+40}{(4t^2+1)^4}$$

I've spend more than a hour trying to decrypt and decompose the polynomial, but to no avail. For simple cubic polynomial I know it might be possible to try ##-1## or ##1## or the factor of the lowest term to get the correct linear factor, which can then be used to do long division to get the other factor if there's any.

Eventually I thought it's the end of the line, but then when I checked to WA. the nominator decomposed to this.

$$8(4 t^2+1)(4 t^2+4 t+5)$$

How can we know the factor if it's not linear i.e ##(x-a)##? For the note I'm currently reading the Complex Numbers section in Boas book. So far the author has not discussed yet techniques to factor polynomial like this.

Thank You

I'd like to ask you how to efficiently factorize complicated polynomial like this one for example:

$$\frac{128t^4+128t^3+192t^2+32t+40}{(4t^2+1)^4}$$

I've spend more than a hour trying to decrypt and decompose the polynomial, but to no avail. For simple cubic polynomial I know it might be possible to try ##-1## or ##1## or the factor of the lowest term to get the correct linear factor, which can then be used to do long division to get the other factor if there's any.

Eventually I thought it's the end of the line, but then when I checked to WA. the nominator decomposed to this.

$$8(4 t^2+1)(4 t^2+4 t+5)$$

How can we know the factor if it's not linear i.e ##(x-a)##? For the note I'm currently reading the Complex Numbers section in Boas book. So far the author has not discussed yet techniques to factor polynomial like this.

Thank You

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