Question

Your friend claims that when a polynomial function has a leading coeffcient of 1 and the coefficients are all integers , every possible rational zero is an integer . Is your friend correct ? Explain your reasoning.

Answer 1

Using the rational root theorem, it is found that your friend is correct.

What is the rational root theorem?

• It is a theorem that states that for a polynomial with integer coefficients, with q being the factors of the leading coefficient and p being the factors of the constant, every possible rational root is the format $\frac{p}{q}$.

In this problem:

• The leading coefficient is 1, hence it's only factor is $q = 1$, thus guaranteeing that every possible rational zero is an integer, which means that your friend is correct.

To learn more about the rational root theorem, you can take a look at brainly.com/question/10937559