Polynomial Remainder & Synthetic Division Challenge

A farmer has a rectangular field represented by the polynomial A(x) = x^2 + 5x + 6. If he wants to divide the field into two equal parts, what polynomial represents the area of each part?

• (1/2)x^2 + (5/2)x + 3

• x^2 + 5x + 6

• (1/2)x^2 + 3x + 2

• (1/4)x^2 + (5/4)x + 1.5

A school is organizing a fundraiser and has a goal of raising P(x) = 2x^3 - 3x^2 + 4x - 5 dollars. If they have already raised $10, what will be the remainder when P(x) is divided by (x - 5)?

• 100

• 220

• 150

• 190

A company produces a product with a profit function given by P(x) = x^3 - 6x^2 + 9x. Use synthetic division to find the profit when they produce 3 units.

• 0

• 3

• 6

• -1

A polynomial representing the height of a projectile is given by H(t) = -16t^2 + 64t + 48. What is the height of the projectile at t = 2 seconds using synthetic division?

• 112

• 96

• 80

• 128

A car rental company has a revenue function R(x) = 3x^4 - 12x^3 + 9x^2 - 4. If they want to find the revenue when they rent out 2 cars, what is the remainder when R(x) is divided by (x - 2)?

• -4

• -16

• 0

• -8

A local bakery sells cupcakes represented by the polynomial C(x) = x^3 - 4x^2 + 6x - 8. If they sell 1 dozen cupcakes, what is the value of C(12) using synthetic division?

• 1216

• 900

• 1000

• 1500

A construction company has a volume function V(x) = x^3 - 3x^2 + 2x. If they want to find the volume when x = 1, what is the remainder when V(x) is divided by (x - 1)?

• 1

• -1

• 0

• 2

A polynomial representing the cost of materials is C(x) = 4x^3 - 2x^2 + 3x - 1. If the company uses 3 units of material, what is the cost using synthetic division?

• 75

• 120

• 85

• 98

A local theater has a ticket sales function S(x) = x^4 - 5x^3 + 6x^2 - 2. What is the remainder when S(x) is divided by (x - 2) to find ticket sales when 2 tickets are sold?

• -2

• 0

• -6

• 4

A polynomial representing the distance traveled by a car is D(t) = 5t^3 - 15t^2 + 10t. If the car travels for 3 hours, what is the distance using synthetic division?

• 60

• 30

• 15

• 45