Zeros of Polynomials

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

How is the degree of a polynomial related to its factors?

Back

The degree of a polynomial is equal to the number of its linear factors, counting multiplicities.

Front

What does it mean for a polynomial to have a zero?

Back

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

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 the variable.

Front

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

Back

The number of factors of a polynomial (counting multiplicities) is equal to its degree.

Front

If a polynomial has a factor of (x - a), what does this imply?

Back

If a polynomial has a factor of (x - a), then x = a is a zero of the polynomial.

Front

What is the multiplicity of a zero?

Back

The multiplicity of a zero refers to the number of times a particular zero is repeated as a factor of the polynomial.

Front

Can a polynomial have complex zeros?

Back

Yes, polynomials can have complex zeros, and they occur in conjugate pairs if the coefficients are real.

Front

What is the degree of the polynomial (x - 1)(x + 5)?

Back

The degree of the polynomial (x - 1)(x + 5) is 2.

Front

If a polynomial has a degree of 3, what is the maximum number of zeros it can have?

Back

A polynomial of degree 3 can have a maximum of 3 zeros.