Unit Test — Unit test Answers

A polynomial function has a root of –3 with multiplicity 2, a root of 0 with multiplicity 1, a root of 1 with multiplicity 1, and a root of 3 with multiplicity 2. If the function has a positive leading coefficient and is of even degree, which could be the graph of the function?

Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?

Use synthetic division to solve (x4 – 1) ÷ (x – 1). What is the quotient?

Which statement about the simplified binomial expansion of (a – b)n, where a, b and n are positive integers, is true?

According to the Rational Root Theorem, which is a factor of the polynomial f(x) = 3x3 – 5x2 – 12x + 20?

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x3 – 7x + 11?

What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 + i?

The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly’s reasoning is correct or incorrect?

Which of the following describes the roots of the polynomial function ?

Which polynomial function has a leading coefficient of 1, roots –2 and 7 with multiplicity 1, and root 5 with multiplicity 2?

Mark is solving an equation where one side is a quadratic expression and the other side is a linear expression. He sets the expressions equal to y and graphs the equations. What is the greatest possible number of intersections for these graphs?

What is the fifth term in the binomial expansion of (x + 5)8?

What are the possible degrees for the polynomial function?

Three roots of a fifth degree polynomial function f(x) are –2, 2, and 4 + i. Which statement describes the number and nature of all roots for this function?

Becca graphs the equations y = –3(x – 1) and y = x – 5 to solve the equation –3(x – 1) = x – 5. Her graph is shown below.What are the solution(s) of –3(x – 1) = x – 5?

The owner of a coffee shop chain creates a graph representing sales in thousands of dollars. She describes the characteristics as follows:• There have been two turning points in sales this year.• Sales are expected to increase in the long run.• The least amount of sales during the year is about $250,000.Which graph correctly shows the coffee shop’s sales?

A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation can be used to find x. What was the side length of the original cube? Use a graphing calculator and a system of equations to find the answer.

If f(–2) = 0, what are all the factors of the function ? Use the Remainder Theorem.

Russ is solving an equation where both sides are linear expressions. He sets the expressions equal to y and graphs the system finding that they are the same line. How should Russ interpret this outcome?

What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.