Answer: The required polynomial in standard form is [tex]x^2-6x^2+11x-6.[/tex]
Step-by-step explanation: We are given to write a polynomial in standard form with zeroes 1, 2 and 3.
We know that
if a polynomial p(x) has zeroes at a, b and c, then its expression can be written as follows :
[tex]p(x)=(x-a)(x-b)(x-c).[/tex]
Therefore, if f(x) represents the given polynomial, then we must have
[tex]f(x)\\\\=(x-1)(x-2)(x-3)\\\\=(x^2-3x+2)(x-3)\\\\=x(x^2-3x+2)-3(x^2-3x+2)\\\\=x^3-3x^2+2x-3x^2+9x-6\\\\=x^2-6x^2+11x-6.[/tex]
Thus, the required polynomial in standard form is [tex]x^2-6x^2+11x-6.[/tex]
