Synthetic Division and the Remainder Theorem

Question 1

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, (x + 3) is a factor of the polynomial. Divide 2x^3 + 9x^2 + 7x – 6 by (x + 3) using synthetic division. The resulting quotient is the quadratic expression 2x^2 + 3x – 2. Finally, f

Question 2

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

Revolt · Accepted Answer

Identify the factor x + 3 from the given root –3.

Question 3

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

Revolt · Accepted Answer

–2; –4; 4

Question 4

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

P = –10x3 + 40x

Question 5

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 main errors in the synthetic division setup. First, they used -5 instead of 5 as the value for k (the divisor should be 5 since the factor is x - 5). Second, they did not use a placeholder zero for the missing x^2 term in the polynomial. If the division is performed correctly, the remainder is 0, which means x - 5 is indeed a factor of the polynomial.

Question 6

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. ⇒ 1.3 million bicycles

Revolt · Accepted Answer

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Synthetic Division and the Remainder Theorem Answers

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