Question

explain why the terms of the polynomial ( y^2 + 7 ) are said to be relatively prime.

choose the correct answer below.

a. the terms 7 and ( y^2 ) are prime numbers.

b. the two terms of the polynomial share common factors only when ( y ) is a multiple of 7.

c. the numbers 7 and 1 are prime numbers.

d. the two terms of the polynomial share no common factors other than 1.

Explanation:

Two terms are relatively prime if their only common positive integer factor is 1. For the polynomial $y^2 + 7$, the first term $y^2$ has factors of $y$ and 1, while the second term 7 has factors of 7 and 1. There are no other shared factors besides 1. Option A is wrong because $y^2$ is not a prime number. Option B is incorrect as the terms never share a common factor besides 1 regardless of $y$. Option C is irrelevant since 1 is not a prime number.

Answer:

D. The two terms of the polynomial share no common factors other than 1.