Zeros & Multiplicity (Alg 2 Friendly)

Front

What are the zeros of the polynomial function? y = x(x - 6)(x + 5)

Back

The zeros are 0, 6, and -5.

Front

What are the zeros of the polynomial y = 3(x + 4)(x + 1)(x - 3)?

Back

The zeros are -4, -1, and 3.

Front

How does a multiplicity of 3 affect the graph?

Back

It causes the graph to squiggle (change direction) at the zero.

Front

Write a function rule for a polynomial with zeros at -1, 2, and 7 (all multiplicity of 1).

Back

f(x) = (x + 1)(x - 2)(x - 7).

Front

If the graph does not cross the x-axis, what does that mean about the multiplicity of that zero?

Back

It means the multiplicity is even (2, 4).

Front

Define 'zero' in the context of polynomial functions.

Back

A zero of a polynomial function is a value of x that makes the function equal to zero.

Front

What is multiplicity in relation to polynomial zeros?

Back

Multiplicity refers to the number of times a particular zero is repeated in a polynomial.

Front

How does a zero with odd multiplicity affect the graph?

Back

A zero with odd multiplicity causes the graph to cross the x-axis at that point.

Front

How does a zero with even multiplicity affect the graph?

Back

A zero with even multiplicity causes the graph to touch the x-axis but not cross it.

Front

What is the relationship between the degree of a polynomial and the number of zeros?

Back

The degree of a polynomial is equal to the maximum number of zeros it can have.