PreCalculus Practice Flashcard 2.4

Front

Find all zeros for the polynomial function P(x)= x^3 - 3x^2 + 12x - 10

Back

1, 1-3i, 1+3i

Front

A polynomial function with rational coefficients of degree 4 MUST have at least 1 rational zero. True or False?

Back

False

Front

How many zeros does the polynomial function P(x) = 3x^4 + 4x - 8 have?

Back

4

Front

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

Back

P(x) = x^3 + 2x^2 + 9x + 18

Front

Find all zeros of the polynomial function P(x) = x^3 + 6x^2 + 9x + 54.

Back

-6, 3i, -3i

Front

What is the Fundamental Theorem of Algebra?

Back

Every non-constant polynomial function has at least one complex root.

Front

Define a polynomial function.

Back

A function that can be expressed in the form P(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where a_n, a_{n-1}, ..., a_0 are constants.

Front

What is a zero of a polynomial function?

Back

A value of x for which P(x) = 0.

Front

What is the degree of a polynomial?

Back

The highest power of the variable in the polynomial.

Front

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

Back

A polynomial of degree n can have at most n zeros.