Given any​ polynomial, without​ graphing, how can you determine how many possible zeros​ (x intercepts) the polynomial will​ have? Please provide an example.

Answer 1

To determine the number of possible zeros (x-intercepts) a polynomial will have, we can use the fundamental theorem of algebra. According to this theorem, a polynomial of degree n will have exactly n complex zeros, counting multiplicities.

For example, let's consider the polynomial f(x) = x^3 + 2x^2 - 5x - 6. The degree of this polynomial is 3, so we can expect it to have exactly 3 possible zeros.

However, factoring a polynomial to find its zeros can be quite challenging for higher-degree polynomials. In such cases, we can use techniques like the rational root theorem to determine the possible rational zeros.