Question

Write a polynomial function of the least degree with integral coefficients that has the given zeros: 2, -1/5, -2.

A. f(x) = 5x^3 - 7x^2 + 2x - 2
B. f(x) = (5x - 2)(x + 2)(5x + 1)
C. f(x) = 10x^3 + x^2 - 4x - 1
D. f(x) = (x - 2)(5x + 1)(5x + 2)

Answer 1

The polynomial function with the given zeros is (x - 2)(5x + 1)(5x + 10).

Step-by-step explanation:

To find a polynomial function of the least degree with integral coefficients that has the given zeros, we can write the function in factored form using the zeros.

The zeros are 2, -1/5, and -2, so the factored form of the polynomial function is (x - 2)(x + 1/5)(x + 2).

We can simplify this by finding a common denominator for the fractions and multiplying:

(x - 2)(5x + 1)(5x + 10).

This polynomial function has integral coefficients and is of the least degree possible.