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

Answer 1

A polynomial function with zeroes at 1, 2, -2, and -3 can be written in factored form as:

f(x) = (x - 1)(x - 2)(x + 2)(x + 3)

Expanding this expression gives:

f(x) = (x^2 - 2x - x + 2)(x^2 + 3x + 2x + 6)
f(x) = (x^2 - 3x + 2)(x^2 + 5x + 6)
f(x) = x^4 + 5x^3 + 6x^2 - 3x^3 - 15x^2 - 18x + 2x^2 + 10x + 12

Combining like terms, we get the polynomial function in standard form:

f(x) = x^4 + 2x^3 - 7x^2 - 8x + 12