Question

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. -1,2,3

Answer 1

x^3-4x^2+x+6=0

Answer 2

Can you explain please?

Answer 3

it works out as follows
x^3-(sum of zeroes)x^2+(sum of products of zeroes taken two at a time)x-(products of zeroes)=0

Answer 4

another way to look at this is: if x0 is a zero of f(x) then x-x0 factors f(x).

so if -1, 2 and 3 are ALL the zeros of the polynomial then
\[ \large f(x)=(x-(-1))(x-2)(x-3)=(x+1)(x-2)(x-3) \]
u just have to multiply.