Synthetic Division and the Remainder Theorem — Unit test Answers

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

What is the factored form of ?

Which expression is a possible leading term for the polynomial function graphed below?

A cube with side length is stacked on another cube with side length . What is the total volume of the cubes in factored form?

What are the possible degrees for the polynomial function?

A polynomial function has a root of –6 with multiplicity 1, a root of –2 with multiplicity 3, a root of 0 with multiplicity 2, and a root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree, which statement about the graph is true?

What is the completely factored form of f(x) = 6x3 – 13x2 – 4x + 15?

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

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 is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots and 2?

The price that a company charged for a basketball hoop is given by the equation where x is the number of hoops that are produced, in millions. It costs the company $30 to make each basketball hoop. The company recently reduced its production to 1 million hoops but maintained its profit of 15 million dollars. Approximately how many basketball hoops did the company previously produce to make the same profit?

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

What are the solutions of the equation (2x + 3)2 + 8(2x + 3) + 11 = 0? Use u substitution and the quadratic formula to solve.

What are the solutions of the equation (x – 3)2 + 2(x – 3) – 8 = 0? Use u substitution to solve.

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

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

Let a, b, and c be real numbers where a b c 0. Which of the following functions could represent the graph below?

Which statement best describes the equation (x + 5)2 + 4(x + 5) + 12 = 0?

If (x – 2k) is a factor of f(x), which of the following must be true?

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