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

A. X^4+2x^3+7^2-8x+12
B. X^4+2x^3-7^2-8x+12
C. X^4+2x^3-7^2+8x+12
D. X^4+2x^3+7^2+8x+12

I’m guessing B but I’m honestly not sure on what I’m doing

To find a polynomial function in standard form with zeros 1, 2, -2, and -3, you can use the zero-product property.

The zero-product property states that if a polynomial function is equal to zero, then one of its factors must be equal to zero. So if the zeros are 1, 2, -2, and -3, then the factors would be (x - 1), (x - 2), (x + 2), and (x + 3) respectively.

By multiplying these factors together, you can obtain the polynomial function in standard form.

Let's multiply them:
(x - 1)(x - 2)(x + 2)(x + 3)

Expanding this expression, we get:
(x^2 - 3x + 2)(x^2 + 5x + 6)

Further expanding this expression, we get:
(x^2 * x^2) + (x^2 * 5x) + (x^2 * 6) + (-3x * x^2) + (-3x * 5x) + (-3x * 6) + (2 * x^2) + (2 * 5x) + (2 * 6)

Simplifying this expression, we get:
x^4 + 5x^3 + 6x^2 - 3x^3 - 15x^2 - 18x + 2x^2 + 10x + 12

Combining like terms, we get:
x^4 + 2x^3 - 7x^2 - 6x + 12

Comparing this result with the given choices, we can see that option B, X^4+2x^3-7^2-8x+12, is the correct answer.

Your function would be:

f(x) = (x-1)(x-2)(x+2)(x+3)
= (x^2 - 4)(x-1)(x+3)

expand it further to see which one matches.
That way you will not have to "guess" what the correct version is.