Unit Test

One root of a third degree polynomial function f(x) is -5 + 2i. Which statement describes the number and nature of all roots for this function?

f(x) has two complex roots and one real root.

The area of a rectangle is (x3 - 5x2 + 3x - 15), and the width of the rectangle is (x2 + 3). If area = length × width, what is the length of the rectangle?

x - 5

What is the completely factored form of ?

(2x - 5)(3x + 1)

What is the completely factored form of 12xy - 9x - 8y + 6?

(3x - 2)(4y - 3)

Which statement about 4x2 + 19x - 5 is true?

One of the factors is (x + 5).

The price that a company charged for a computer accessory is given by the equation where x is the number of accessories that are produced, in millions. It costs the company $10 to make each accessory. The company currently produces 2 million accessories and makes a profit of 100 million dollars. What other number of accessories produced yields approximately the same profit?

1.45 million

What is the quotient of (2x4 - 3x3 - 3x2 + 7x - 3) ÷ (x2 - 2x + 1)?

2x2 + x - 3

A polynomial function has a root of -7 with multiplicity 2, a root of -1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1. If the function has a positive leading coefficient and is of even degree, which statement about the graph is true?

The graph of the function is positive on (, -7).

If (x + k) is a factor of f(x), which of the following must be true?

f(-k) = 0

Which of the following is the complete list of roots for the polynomial function of f(x)=(x^2 + 2x -15)(x^2+8x+17)?

-5, 3, -4 + i, -4 - i

According to the Rational Root Theorem, the following are potential roots of f(x) = 6x4 + 5x3 - 33x2 - 12x + 20.

-5/2

What is the end behavior of the graph of the polynomial function f(x) = -x5 + 9x4 - 18x3?

Negative Positive Positive Negative

Anja divides (8x3 - 36x2 + 54x - 27) by (2x - 3) as shown below. What error does Anja make?

She makes a multiplication error.

Which second degree polynomial function has a leading coefficient of 2 and roots -3 and 5?

f(x) = 2x2 - 4x - 30

Which statement about the polynomial function g(x) is true?

If the leading coefficient of g(x) is 1, all rational roots of g(x) = 0 must be integers.