Synthetic Division and the Remainder Theorem

Question 1

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

Revolt · Accepted Answer

x + 3

Question 2

Dividend:

Revolt · Accepted Answer

2x3 + 11x2 + 18x + 9

Question 3

Quotient:

Revolt · Accepted Answer

2x2 + 5x + 3

Question 4

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.

Revolt · Accepted Answer

x2 – 2x – 9

Question 5

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

Revolt · Accepted Answer

x + 4; x – 1; x + 2

Question 6

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 7

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 8

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 9

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

Revolt · Accepted Answer

–2; –4; 4

Question 10

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

Synthetic Division and the Remainder Theorem Answers

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