Precalc Polynomial graphs

Front

What are the zeros of the polynomial f(x) = (x+2)(x-3)²(x-4)?

Back

The zeros are -2, 3 (multiplicity 2), and 4.

Front

What does it mean for a root to have a multiplicity of 2?

Back

A root with a multiplicity of 2 means that it is a repeated root, and the graph touches the x-axis at that point but does not cross it.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by the leading term's degree and leading coefficient.

Front

What is the leading coefficient of the polynomial f(x) = 2x³ - 5x² + 3?

Back

The leading coefficient is 2.

Front

What is the factored form of the polynomial f(x) = x² - 5x + 6?

Back

The factored form is f(x) = (x-2)(x-3).

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the highest power of x and determines the number of zeros and the end behavior.

Front

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

Back

To find the x-intercepts, set the polynomial equal to zero and solve for x.

Front

What is the relationship between the multiplicity of a root and the graph's behavior at that root?

Back

If a root has an odd multiplicity, the graph crosses the x-axis; if it has an even multiplicity, the graph touches the x-axis.

Front

What is the factored form of f(x) = x³ - 3x² - 4x + 12?

Back

The factored form is f(x) = (x-2)(x+2)(x-3).

Front

How can you determine if a polynomial is in standard form?

Back

A polynomial is in standard form when its terms are arranged in descending order of degree.