Synthetic Division and the Remainder Theorem

Dividend:

A

Find the quotient.(5x4 - 3x2 + 4) ÷ (x + 1)

A

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?

B

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.

C

Quotient:

D

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

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

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

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

B

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.

Recognize that the student used k = -5 instead of k = 5. Recognize that the student did not use a placeholder zero for the x2 term. Conclude that x - 5 is a factor because there is no remainder when the division is performed correctly

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

D