Question

Write a polynomial function of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.

-1, 2, 4

Answer 1

9514 1404 393

Answer:

f(x) = x³ -5x² +2x +8

Explanation:

If the function has a zero of p, then it has a factor of (x-p). The polynomial of least degree will only have factors corresponding to the given zeros:

f(x) = (x -(-1))(x -2)(x -4)

= (x +1)(x -2)(x -4)

= (x² -x -2)(x -4)

f(x) = x³ -5x² +2x +8