Polynomial Zeros and Multiplicity

Front

What effect do even multiplicities have on the x-axis?

Back

Even multiplicities cause the graph to touch the x-axis and bounce back.

Front

What does it mean if a zero crosses the x-axis?

Back

A zero that crosses the x-axis indicates an odd multiplicity.

Front

What does it mean if a zero turns at the x-axis?

Back

A zero that turns at the x-axis indicates an even multiplicity.

Front

What is the factored form of a polynomial?

Back

The factored form expresses a polynomial as a product of its linear factors.

Front

What are the roots of the polynomial function y = (x + 2)(x - 7)^3?

Back

The roots are -2 and 7 with multiplicity 3.

Front

How do you determine the multiplicity of a root?

Back

The multiplicity of a root is determined by the exponent of the factor in the polynomial.

Front

What is the significance of a root with odd multiplicity?

Back

A root with odd multiplicity crosses the x-axis at that point.

Front

What is the significance of a root with even multiplicity?

Back

A root with even multiplicity touches the x-axis and does not cross it.

Front

How can you identify the multiplicity of a root from a graph?

Back

If the graph touches the x-axis and bounces back, the multiplicity is even; if it crosses, the multiplicity is odd.

Front

What is the general form of a polynomial?

Back

A polynomial is expressed as f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0.