Synthetic Division and the Remainder Theorem

Question 1

Identify the polynomial divisor, dividend, and quotient represented by the synthetic division. Divisor:

Revolt · Accepted Answer

D: x + 3

Question 2

Use synthetic division to find the expression for the area of the base of a rectangular prism with height x + 4 and volume x3 + 2x2 – 17x – 36.

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C: x2 – 2x – 9

Question 3

Find the quotient.(2x4 – 3x3 – 6x2 + 11x + 8) ÷ (x – 2)

Revolt · Accepted Answer

B:

Question 4

Select all of the factors of x3 + 5x2 + 2x – 8.

Revolt · Accepted Answer

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Question 5

One root of f(x) = 2x3 + 9x2 + 7x – 6 is –3. Explain how to find the factors of the polynomial.

Revolt · Accepted Answer

Since -3 is a root, identify x + 3 as a factor and use synthetic division to divide 2x^3 + 9x^2 + 7x - 6 by x + 3. The quotient is 2x^2 + 3x - 2 with remainder 0. Factoring the quotient gives (x + 2)(2x - 1), so the polynomial factors as (x + 3)(x + 2)(2x - 1).

Question 6

Which of the following facts did you include in your explanation? Select all that apply.

Revolt · Accepted Answer

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Question 7

Select all of the roots of x3 + 2x2 – 16x– 32.

Revolt · Accepted Answer

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Question 8

The price received for a bicycle is given by the equation b = 100 – 10x2, where x is the number of bicycles produced, in millions.It costs the company $60 to make each bicycle.What is the profit function for the company?

Revolt · Accepted Answer

B: P = –10x3 + 40x

Question 9

The company recently reduced its production to 1 million bicycles, but maintained its profit of 30 million dollars. What greater number of bicycles had the company previously produced to make the same profit? Round your answer to the nearest tenth. million bicycles

Revolt · Accepted Answer

1.3

Question 10

A student uses the division shown to divide –3x4 + 15x3 – x + 5 by x – 5, and concludes that x – 5 is not a factor of the polynomial. Describe two errors the student made. Is x – 5 a factor? Explain.

Revolt · Accepted Answer

The student made two errors: They used k = -5 instead of k = 5, and they failed to use a placeholder 0 for the missing x^2 term. Using the correct coefficients -3, 15, 0, -1, 5 and k = 5 gives a remainder of 0, so x - 5 is a factor.

Synthetic Division and the Remainder Theorem Answers

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