Effect of Constant Term on Polynomial Roots

Question

In an experiment analyzing the polynomial $$f(x)= x^3 - 2*x^2 - x + 2$$, researchers study its roots and sign changes over different intervals. What would happen if the constant term were increased to modify the polynomial to $$x^3 - 2*x^2 - x + 3$$?

Accepted Answer

The locations of the roots would change, which in turn would alter the intervals where the polynomial is positive or negative.

Answer

The polynomial would have the same roots, with the graph merely shifting upward without affecting sign changes.

Answer

The behavior at the boundaries would remain identical because the constant term does not influence end behavior.

Answer

The degree of the polynomial would effectively increase, resulting in additional turning points.