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

A. g (x) = x4 + 3x3 - 7x2 - 15x + 18

B. g (x) = x4 + 3x3 - 7x2 + 2x + 18

C. g (x) = x4 - 3x3 + 7x2 + 15x + 18

D. g (x) = x4 - 3x3 - 7x2 + 15x + 18

Hello,

(x-1) (x-2) (x+3) ² = (x²-3x+2) (x²+6x+9)

=x^4+3x^3-7x²-15x+18

Answer A

The zeroes are 1, 2, - 3 and - 3

we can make the zeroes into factors of

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

Multiply all the factors in order to get the polynomial function

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

g (x) = x4 + 3x3 - 7x2 - 15x + 18

So the correct answer is letter A. g (x) = x4 + 3x3 - 7x2 - 15x + 18