Answer:
[tex]f(x) = x^4 -3x^3-7x^2+27x-18[/tex]
Step-by-step explanation:
We are given the following information in the question:
A polynomial have zeroes: 1,2,3, -3
Thus, we can write:
[tex](x-1),(x-2),(x-3),(x+3)[/tex]
are factors of the given polynomial.
Let f(x) be the polynomial.
Thus,
[tex]f(x) = (x-1)(x-2)(x-3)(x+3)\\\text{Identity: }(a+b)(a-b)=(a^2-b^2)\\= (x-1)(x-2)(x^2-9)\\=(x-1)(x^3-9x-2x^2+18)\\=(x-1)(x^3-2x^2-9x+18)\\= x^4 - 2x^3-9x^2+18x-x^3+2x^2+9x-18\\f(x) = x^4 -3x^3-7x^2+27x-18[/tex]
f(x) is the required polynomial.
