Polynomials in Factored Form

Front

What is a polynomial in factored form?

Back

A polynomial expressed as a product of its linear factors, e.g., f(x) = (x - r1)(x - r2)...(x - rn) where r1, r2, ..., rn are the roots.

Front

How do you find the roots of a polynomial?

Back

Set the polynomial equal to zero and solve for x. The solutions are the roots.

Front

What is the significance of the degree of a polynomial?

Back

The degree indicates the highest power of x in the polynomial, which determines the number of roots and the behavior of the graph.

Front

What does it mean for a polynomial to have a root of multiplicity?

Back

A root has multiplicity m if it can be factored m times from the polynomial. It affects the graph's behavior at that root.

Front

What is the behavior of a graph at a root with odd multiplicity?

Back

The graph crosses the x-axis at the root.

Front

What is the behavior of a graph at a root with even multiplicity?

Back

The graph touches the x-axis and bounces back at the root.

Front

How do you determine the x-intercepts of a polynomial function?

Back

Set the polynomial equal to zero and solve for x. The solutions are the x-intercepts.

Front

What is the factored form of a polynomial with roots -1, 1, and 4?

Back

f(x) = (x + 1)(x - 1)(x - 4)