Sect. 5.1 Writing Polynomial Functions given Zeros

Front

What is the relationship between imaginary roots in polynomial functions?

Back

All imaginary roots come in pairs.

Front

Write the polynomial in standard form given the zeros: x = -2, 1, 4.

Back

f(x) = x³ - 3x² - 6x + 8

Front

Find a polynomial function of degree 3 with zeros 3i and -2.

Back

P(x) = x³ + 2x² + 9x + 18

Front

If 3i is a root of a polynomial, what is the corresponding root?

Back

-3i

Front

What is the standard form of a polynomial?

Back

A polynomial is in standard form when it is expressed as a sum of terms in descending order of degree.

Front

How do you find a polynomial given its zeros?

Back

Use the zeros to create factors of the form (x - zero) and multiply them.

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 is a zero of a polynomial?

Back

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

Front

What is the significance of complex roots in polynomials?

Back

Complex roots occur in conjugate pairs, ensuring that polynomials with real coefficients have an even number of non-real roots.

Front

How do you determine the number of zeros a polynomial can have?

Back

A polynomial of degree n can have up to n zeros.