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

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

f(x) = x^6 + ... + 36 with a leading coefficient 1, constant term 36 and also x^5, x^4, x^3, x^2 and x terms when you multiply the 3 quadratic factors together. the coefficients of each term are rational and integers

f(x) has degree 6 which is the least possible

the 3 zeros each have multiplicity 2

if you graphed the polynomial, it would have 3 points of tangency with the x axis