Unit 4 Polynomials Test Review

Front

How many zeros does the polynomial function f(x) = x^5 - 3x^3 + x have?

Back

5

Front

Find all the zeros of the cubic function f(x) = x^3 - 4x^2 + 5x - 2. List any repeating zeros.

Back

{2, 1 mult 2}

Front

Solve the equation: b^3 - 10b^2 + 9b = 0.

Back

b = 0, b = 1, and b = 9

Front

What is the product of (2x + 2)(4x^2 + 4)?

Back

16x^3 + 28x^2 + 28x + 16

Front

True or False: All imaginary roots come in pairs.

Back

True

Front

Define a polynomial function.

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is the degree of the polynomial f(x) = 3x^4 - 5x^2 + 2?

Back

4

Front

Explain the Fundamental Theorem of Algebra.

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial function of degree n has exactly n roots in the complex number system, counting multiplicities.

Front

What is a zero of a polynomial function?

Back

A zero of a polynomial function is a value of x for which the function f(x) equals zero.

Front

How do you find the zeros of a polynomial function?

Back

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