Unit Test Answers

Tomas learned that the product of the polynomials (a + b)(a2 – ab + b2) was a special pattern that would result in a sum of cubes, a3 + b3. His teacher put four products on the board and asked the class to identify which product would result in a sum of cubes if a = 2x and b = y.

What is the sum of the polynomials?(7x3 – 4x2) + (2x3 – 4x2)

Use synthetic division to solve (x4 – 1) ÷ (x – 1). What is the quotient?

The price that a company charged for a basketball hoop is given by the equation where x is the number of hoops that are produced, in millions. It costs the company $30 to make each basketball hoop. The company recently reduced its production to 1 million hoops but maintained its profit of 15 million dollars. Approximately how many basketball hoops did the company previously produce to make the same profit?

Which will result in a difference of squares?

What is the quotient?x + 1)3x2 − 2x + 7

What is the quotient?

Zohar is using scissors to cut a rectangle with a length of 5x – 2 and a width of 3x + 1 out of a larger piece of paper. Which expression can be used to find the perimeter of the rectangle and what is the perimeter if x = 4?

The formula for the area of a parallelogram is A = bh, where b is the base and h is the height.

The table represents the multiplication of two binomials.

Randy divides (2x4 – 3x3 – 3x2 + 7x – 3) by (x2 – 2x + 1) as shown below. What error does Randy make?

What is the remainder when (x4 + 36) is divided by (x2 – 8)?

Simplify the expression –2(p + 4)2 – 3 + 5p. What is the simplified expression in standard form?

The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?

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

What is the product of (2p + 7)(3p2 + 4p – 3)?

If (x – 2k) is a factor of f(x), which of the following must be true?

The revenue, in dollars, of a company that makes toy cars can be modeled by the polynomial 3x2 + 4x – 60. The cost, in dollars, of producing the toy cars can be modeled by 3x2 – x + 200. The number of toy cars sold is represented by x.

What is the difference of the polynomials?(8r6s3 – 9r5s4 + 3r4s5) – (2r4s5 – 5r3s6 – 4r5s4)

Which term completes the product so that it is the difference of squares?(−5x−3)(−5x+________)

Adi used algebra tiles to represent the product .

The first step when dividing 9m2 − 4m − 6 by 3m is shown. Which could be the next step?

If f(–2) = 0, what are all the factors of the function ? Use the Remainder Theorem.

The revenue, in dollars, of a company that produces jeans can be modeled by 2x2+17x−175. The cost, in dollars, of producing the jeans can be modeled by 2x2−3x−125. The number of pairs of jeans that have been sold is represented by x. If the profit is the difference between the revenue and the cost, which expression can be used to find profit and what is that profit when 75 pairs of jeans are sold?

Manuel's division is shown.