What is a polynomial function in standard form with zeros 1, 2, -2, and -3?(1 point)
Responses
A. x4+2x3−7x2+8x+12
B. x4+2x3−7x2−8x+12
C. x4+2x3+7x2+8x+12
D. x4+2x3+7x2−8x+12
To answer this question, we need to recall that the zeros of a polynomial function are the values of x for which the function equals zero.
Given that the zeros are 1, 2, -2, and -3, we can write the factors of the polynomial as (x-1)(x-2)(x+2)(x+3).
To find the polynomial function in standard form, we multiply these factors:
(x-1)(x-2)(x+2)(x+3) = (x^2-x-2)(x^2+5x+6)
= x^4 + 5x^3 + 6x^2 - x^3 - 5x^2 - 6x - 2x^2 - 10x - 12
= x^4 + 4x^3 - x^2 - 16x - 12
Therefore, the correct answer is option B: x^4 + 2x^3 - 7x^2 - 8x + 12.