Question

What is the standard form of `y= (x-5)(x-2)(x-1)`?

Answer 1

`y = x^3-8x^2+17x-10`

Explanation:

Note that:

`(x-alpha)(x-beta)(x-gamma)`

`=x^3-(alpha+beta+gamma)x^2+(alphabeta+betagamma+gammaalpha)x-alphabetagamma`

So with `alpha=5`, `beta=2` and `gamma=1` we find:

`(x-5)(x-2)(x-1) = x^3-8x^2+17x-10`