Given the zeros, write a polynomial function of least degree with integral coefficients

Question

Given the zeros, write a polynomial function of least degree with integral coefficients

2, 4, -1

Answer 1

Hello Alyssa,

When a zero of a polynomial is c, the corresponding factor is (x - c).

Since there are three zeros with no repetition, we expect a 3rd degree polynomial.

Given the zeros 2, 4, -1, the factors are as follow:

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

P(x) = (x² - 6x + 8)(x + 1) FOIL the first 2 factors, then multiply that result times (x + 1)

P(x) = x³ - 5x² + 2x + 8

Regards,

Anita A.