Question

What is a polynomial function in standard form with zeros 1,2,3 and -3

Answer 1

Explanation:

Answer 2

`f(x) = x^4 -3x^3-7x^2+27x-18`

Explanation:

We are given the following information in the question:

A polynomial have zeroes: 1,2,3, -3

Thus, we can write:

`(x-1),(x-2),(x-3),(x+3)`

are factors of the given polynomial.

Let f(x) be the polynomial.

Thus,

`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`

f(x) is the required polynomial.