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Factorize: x^6-7x^3-8...

Factorize: `x^6-7x^3-8`

Text Solution

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Putting `x^3=y` , we get
`(x^6-7x^3-8)`
`=(y^2-7y-8)`
`=(y^2-8y+y-8)=y(y-8)+(y-8)`
` =(y-8)(y+1)`
`=(x^3-8)(x^3+1)`
`=(x^3-2^3)(x^3+1^3)`
` =(x-2)(x^2+2x+4)(x+1)(x^2-x+1)`
` =(x-2)(x+1)(x^2+2x+4)(x^2-x+1)`
`therefore (x^6-7x^3-8)=(x-2)(x+1)(x^2+2x+4)(x^2-x+1)`.
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