Synthetic Division and the Remainder Theorem — Unit test Answers

If (x – 5) is a factor of f(x), which of the following must be true?

Anja divides (8x3 – 36x2 + 54x – 27) by (2x – 3) as shown below. What error does Anja make?

What is the remainder when (3x3 – 2x2 + 4x – 3) is divided by (x2 + 3x + 3)?

The price that a company charged for a computer accessory is given by the equation where x is the number of accessories that are produced, in millions. It costs the company $10 to make each accessory. The company currently produces 2 million accessories and makes a profit of 100 million dollars. What other number of accessories produced yields the same profit?

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

The area of a rectangle is (x3 – 5x2 + 3x – 15), and the width of the rectangle is (x2 + 3). If area = length × width, what is the length of the rectangle?

What is the difference of the two polynomials?(7y2 + 6xy) – (–2xy + 3)

If f(–5) = 0, what are all the factors of the function ? Use the Remainder Theorem.

What is the quotient of (2x4 – 3x3 – 3x2 + 7x – 3) ÷ (x2 – 2x + 1)?

The variables X, Y, and Z represent polynomials where X = a, Y = 3a – 5, and Z = a2 + 2. What is X2Y – Z in simplest form?

The polynomial 8x2 – 8x + 2 – 5 + x is simplified to 8x2 – gx – h. What are the value of g and h?

Profit is the difference between revenue and cost. The revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial 2x3 + 30x – 130. The cost, in dollars, of producing the skateboards can be modeled by 2x3 – 3x – 520. The variable x represents the number of skateboards sold.

What is the product?(5r − 4)(r2 − 6r + 4)

Mrs. Ishimitsu is installing a rubber bumper around the edge of her coffee table. The dimensions of the rectangular table are (2x2 – 16) feet and (–x2 + 4x + 1) feet. Which expression represents the total perimeter of the table, and if x = 3, what is the length of the entire rubber bumper?

What is the polynomial 3y2 + (y + 7)2 – 15 after it has been fully simplified and written in standard form?