Question

Construct a polynomial equation with the following terms: Third-degree, with zeros of −5, −3, and 4, and a y-intercept of −14.

Answer 1

y = (7/12)(x + 5)(x + 3)(x - 4)

Explanation:

1. Start with the factored form of a polynomial equation, y = a(x - p)(x - q)(x - r)..., where a is unknown and p, q, r, etc, are the zeros:
y = a(x - -5)(x - -3)(x - 4) ==> y = a(x + 5)(x + 3)(x - 4)

2. Use the point (0, -14) -- the y-intercept -- as (x, y) in the equation to find a:
y = a(x + 5)(x + 3)(x - 4)
-14 = a(0 + 5)(0 + 3)(0 - 4)
-14 = a(5)(3)(-4)
-14 = -60a
7/12 = a

3. Put number from step 2 into the equation from step 1:
y = (7/12)(x + 5)(x + 3)(x - 4)

If you need to write it in standard form, simply multiply out the factors (FOIL and etc) and distribute the (7/12). I suggest starting to multiply from the (x + 3)(x - 4) first:
`y=(7)/(12)x^3+21x^2-(119)/(12)x-35`.