Question

Explain the difference between finding rational zeros and finding all zeros.

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given the polynomial

$p(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_2x^2+a_1x+a_o$

The rational zeros are all the possible factors of $a_0$ dived by all the possible factors of $a_n$. Therefore we use the rational rots theorem to find all possible rational zeros.

To find all zeros we use the remainder theorem. Thus, we plug in all the rational zeros to determine which ones evaluate to zero. These are the real zeros. We could also use long division to find the remaining zeros as soon as we got the first zero with the remainder theorem.