Finding Polynomial function having leading coefficient

Question

Find a polynomial function​ P(x) having leading coefficient​ 1, least possible​ degree, real​ coefficients, and the given zeros.

4+ sqrt 2, 4− sqrt 2, and 2

Answer 1

Jade

Well if a polynomial P(x) has three roots a, b, c then P(x) = (x-a) (x-b) (x-c)

So all you have to do here is expand (x-4-√2) (x-4+√2) (x-2).

(Multiply the first two brackets together. There will be 9 terms. The terms with √ will cancel out giving a quadratic with integral coefficients and leading coefficient 1. Then multiply this by (x-2)).

Mike