Determine the equation of the following polynomials, using the given information. Write each polynomial in factored form and also in standard form. Don’t forget to solve for a!

A cubic whose zeros are at x = 2, x = -3 and x = 1 and the y-intercept is -12.

-2(x - 2)(x + 3)(x - 1) = 0.

-2x^3 + 14x - 12 = 0.

Step-by-step explanation:

In factored form it is:

f(x) = a(x - 2)(x + 3)(x - 1) = 0

Now, when  x = 0, y = -12 ( the y-intercept) so we have:

-12  = a(0-2)(0+3)(0-1)

6a = -12

a = -2.

The equation in factored form is

-2(x - 2)(x + 3)(x - 1) = 0.

In standard form:

-2(x - 2)(x + 3)(x - 1) = 0.

-2(x - 2)(x^2 + 2x - 3) = 0

-2( x^3 + 2x^2 - 3x - 2x^2 - 4x + 6) = 0

-2(x^3 - 7x + 6) = 0

-2x^3 + 14x - 12 = 0.