Polynomial in Standard Form

Question

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the polynomial in standard form.

−2, 1, 3−2, 1, 3

f(x)=

Answer 1

f(x) = (x+2)^2(x-1)^2(x-3)^2

= (x^2 +4x +4)(x^2 -2x+1)(x^2 -6x +9)

multiply those 3 factors and you get a polynomial

with leading term x^6 and last term 4(1)(9) = 36

and other terms from x to x^5 all having rational integer coefficients