Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.

Third-degree, with zeros of - 4, - 3, and 1, and a y-intercept of - 11.

g (x) = (11/12) x³ + (11/2) x² + (55/12) x - 11

Step-by-step explanation:

A polynomial with zero "a" will have (x - a) as a factor. Your 3rd-degree polynomial will have the three factors ...

... f (x) = (x - (-4)) · (x - (-3)) · (x - 1)

This will have a y-intercept of (4·3· (-1)) = - 12. In order to move it to - 11, we need to vertically scale this function by a factor of 11/12. Then our poynomial is ...

... g (x) = (11/12) (x+4) (x+3) (x-1)

Multiplying this out, you get ...

... g (x) = (11/12) x³ + (11/2) x² + (55/12) x - 11