Question

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

Third-degree, with zeros of -2,-1, and 5, and a y-intercept of -10.

Answer 1

y = x³ -2x² -13x -10

Explanation:

You want a polynomial with x-intercepts -2, -1, and 5, and a y-intercept of -10.

Polynomial factors

A polynomial with zero x = p will have a factor of (x -p). The three given zeros mean factors of the desired polynomial will be ...

p(x) = (x -(-2))(x -(-1))(x -5) = (x +2)(x +1)(x -5)

Expanding this gives ...

p(x) = (x +2)(x² -4x -5) = x³ -2x² -13x -10

This polynomial has a constant of -10, which will be its y-intercept. No additional scaling is needed.

The polynomial function is ...

y = x³ -2x² -13x -10