Adding and Subtracting Polynomials

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?

• 20x−50; $500

• 20x−50; $1,450

• 20x+50; $1,550

• 20x+50; $5,250

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.

• 3x – 260

• 3x + 140

• 5x – 260

• 5x + 140

What is the additive inverse of the polynomial –9xy² + 6x²y – 5x³?

• –9xy² – 6x²y + 5x³

• –9xy² – 6x²y – 5x³

• 9xy² + 6x²y + 5x³

• 9xy² – 6x²y + 5x³

What is the difference of the two polynomials?

(9x² + 8x) – (2x² + 3x)

• 7x² + 5x

• 7x² + 11x

• 11x² + 5x

• 11x² + 11x

What is the sum of the polynomials?

(–x² + 9) + (–3x² – 11x + 4)

• –4x² – 2x + 4

• –4x² – 11x + 13

• 2x² + 20x + 4

• 2x² + 11x + 5

Margot is sewing a ribbon on a seam along the perimeter of a square pillow. The side length of the pillow is 2x²+1 inches. She plans to make a similar pillow, including the ribbon, whose side length is 4x−7 inches. What expression can be used for the length of ribbon that she needs for both pillows, and what is the length if x = 3.5? 

• 2x²+4x−6; 22.0 inches

• 2x²+4x−6; 32.5 inches

• 4(2x²+4x−6;) 88.0 inches

• 4(2x²+4x−6;) 130.0 inches

Pablo folds a straw into a triangle with side lengths of 4x²−3 inches, 4x²−2 inches, and 4x²−1 inches. Which expression can be used to find the perimeter of the triangle, and what is the perimeter when x = 1.5?

• 12x² −6; 21 inches

• 12x²; 27 inches

• 12x² −6; 30 inches

• 12x²; 36 inches

Profit is the difference between revenue and cost. The revenue, in dollars, of a company that manufactures cell phones can be modeled by the polynomial 2x² + 55x + 10. The cost, in dollars, of producing the cell phones can be modeled by 2x² – 15x – 40. The variable x represents the number of cell phones sold.

• 40x – 30; $2,400

• 40x – 30; $9,570

• 70x + 50; $16, 850

• 70x + 50; $28,800

Profit is the difference between revenue and cost. The revenue, in dollars, of a company that manufactures televisions can be modeled by the polynomial 3x² + 180x. The cost, in dollars, of producing the televisions can be modeled by 3x² – 160x + 300. The variable x is the number of televisions sold.

If 150 televisions are sold, what is the profit?

• $2,700

• $6,000

• $50,700

• $51,300

Kat is painting the edge of a triangular stage prop with reflective orange paint. The lengths of the edges of the triangle are (3x – 4) feet, (x² – 1) feet, and (2x² – 15) feet. What is the perimeter of the triangle if x = 4?

• 16 feet

• 40 feet

• 76 feet

• 80 feet