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Factorize x^4-3x^2+2....

Factorize `x^4-3x^2+2`.

Text Solution

Verified by Experts

Putting `x^2=y`, we get
`x^4-3x^2+2`
`=y^2-3y+2, " where" x^2=y`
`=y^2-2y-y+2`
`=y(y-2)-(y-2)`
`=(y-2)(y-1)`
`=(x^2-2)(x^2-1)`
`=(x+sqrt(2))(x-sqrt(2)) (x+1) (x-1)`.
Hence, `(x^4-3x62+2)=(x+sqrt(2)) (x-sqrt(2)) (x+1)(x-1)`.
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