Question

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Third-degree, with zeros of -3,-2, and 1, and a y-intercept of -14.

Answer 1

Recall that the general form of a third-degree polynomial is:

`g(x)=k(x-a)(x-b)(x-c),`

where k is a constant, and a, b, and c are the zeros of the polynomial.

Therefore:

`p(x)=k(x+3)(x+2)(x-1).`

Now, to determine the value of k, we consider the y-intercept:

`p(0)=-14=k(0+3)(0+2)(0-1).`

Solving for k, we get:

`\begin{gathered} -14=-6k, \\ k=-(14)/(-6), \\ k=(14)/(6), \\ k=(7)/(3). \end{gathered}`

Finally:

`p(x)=(7)/(3)(x+3)(x+2)(x-1).`

Answer:

`p(x)=(7)/(3)(x+3)(x+2)(x-1).`