Vocabulary
Zero of a function- The point on the graph of a parabola that the graph intersects the x-axis.
Constant Term- A term that has a number part but no variable part.
Leading Coefficient- The coefficient in the term of a polynomial function that has the greatest exponent.
Constant Term- A term that has a number part but no variable part.
Leading Coefficient- The coefficient in the term of a polynomial function that has the greatest exponent.
Essential Information
The Rational Zero Theorem
If f(x) + anxⁿ + ... + a₁x + a₀ has integer coefficients, then every rational zero of f has the following form:
If f(x) + anxⁿ + ... + a₁x + a₀ has integer coefficients, then every rational zero of f has the following form:
Verifying Zeros
Zeros of polynomial functions can be found when one zero is known. The rational zero theorem is a starting point when no zeros are known.
However, the rational zero theorem only lists possible zeros. In order to find actual zeros of a polynomial function f, the possible zeroes must be tested. This can be done by evaluating the value in f(x) for the test value as x.
Zeros of polynomial functions can be found when one zero is known. The rational zero theorem is a starting point when no zeros are known.
However, the rational zero theorem only lists possible zeros. In order to find actual zeros of a polynomial function f, the possible zeroes must be tested. This can be done by evaluating the value in f(x) for the test value as x.
Limiting the Search for Zeros
When the leading coefficient of the polynomial function is not 1, the list of possible rational zeros can increase dramatically. In such cases, the search can be shortened by sketching the functions graph.
When the leading coefficient of the polynomial function is not 1, the list of possible rational zeros can increase dramatically. In such cases, the search can be shortened by sketching the functions graph.