Question

What is the degree of the simplest polynomial with integer coefficients that has V7, 2, and 2+ 21 as some of

its zeros?

Answer 1

The degree of the simplest polynomial with 7, 2, and 2 + 21 as zeros is 3.

Step-by-step explanation:

The degree of a polynomial is determined by the highest power of the variable in the polynomial. In this case, we are given that the zeros of the polynomial are 7, 2, and 2 + 21. To find the degree of the polynomial, we need to determine the highest power of the variable. Since the zeros are given, we can write the polynomial using these zeros as factors. The simplest polynomial with these zeros is obtained by multiplying the factors together.

Let's start by considering the zero 7. Since it is a zero, we know that x - 7 is a factor of the polynomial. Similarly, x - 2 and x - (2 + 21) = x - 23 are factors of the polynomial.

To find the polynomial, we multiply these factors together: (x - 7)(x - 2)(x - 23). Expanding this expression gives us the polynomial: x^3 - 32x^2 + 311x - 322.

Therefore, the degree of the simplest polynomial with integer coefficients that has 7, 2, and 2 + 21 as zeros is 3.