Polynomial Zeros and Multiplicity Factoring

Front

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

Back

0 (multiplicity of 4), -3 (multiplicity of 2), 2

Front

List the zeros for the function f(x) = (x + 4)(x - 3)(x - 2).

Back

x = -4, x = 3, x = 2

Front

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

Back

0, 6, -5

Front

What is the factored form of the polynomial function with roots at -4, -1 (multiplicity 2), 2, and 4?

Back

f(x) = (x + 4)(x + 1)^2(x - 2)(x - 4)

Front

What are the roots of the polynomial function y = 9(x + 2)(x - 7)^3?

Back

-2, 7 (multiplicity 3)

Front

Define 'zero of a polynomial'.

Back

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

Front

What does 'multiplicity' mean in the context of polynomial zeros?

Back

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

Front

How do you find the zeros of a polynomial in factored form?

Back

Set each factor equal to zero and solve for x.

Front

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

Back

The degree of a polynomial indicates the maximum number of zeros it can have.

Front

Explain how to determine the multiplicity of a zero from a polynomial's factored form.

Back

The multiplicity of a zero is the exponent of the factor corresponding to that zero.