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Need help A-level maths question

https://ibb.co/5HQMF6Z
https://ibb.co/G463DgKT

Can somebody explain how you solve the cubic by inspection for part b? I've managed to do part A but just can't seem to figure out how to factor out the cubic in part b. Any help would be appreciated, thanks.

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by bottled-spiel
https://ibb.co/5HQMF6Z
https://ibb.co/G463DgKT
Can somebody explain how you solve the cubic by inspection for part b? I've managed to do part A but just can't seem to figure out how to factor out the cubic in part b. Any help would be appreciated, thanks.

You know that (2x-1) is a factor, so you divide the polynomial by 2x-1. You can do polynomial division, or how Id do it, farmers field

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