Roots of Polynomials

Front

What is a root of a polynomial?

Back

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

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 will touch the x-axis at that point but not cross it.

Front

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for x.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What effect does a multiplicity of 1 have on the graph of a polynomial?

Back

A root with a multiplicity of 1 causes the graph to cross the x-axis at that root.

Front

What are the zeros of the polynomial y = 5(x + 4)(x + 1)(x - 3)?

Back

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

Front

What is the least degree of the polynomial y = 5(x + 4)(x + 1)(x - 3)?

Back

The least degree is 3.

Front

How does a root with an even multiplicity affect the graph?

Back

A root with an even multiplicity causes the graph to touch the x-axis and bounce back.

Front

What are the roots of the polynomial y = x^3 - 3x^2 - 4x?

Back

The roots are -3, 0, and 3.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial's graph.