Real-Life Applications of Polynomials & Remainder Theorem

A farmer has a rectangular field with a length represented by the polynomial x^2 + 3x - 4 and a width of x - 2. What is the area of the field in terms of x?

• x^3 + x^2 + 8

• x^3 + 2x^2 - 8

• x^2 + 3x + 4

• x^3 - x^2 + 4

A box is constructed such that its volume is given by the polynomial V(x) = x^3 - 5x^2 + 6x. If the height of the box is x - 1, what is the polynomial expression for the base area of the box?

• x^2 - 2x + 3

• x^2 - 3x + 1

• x^2 - 5x + 6

• x^2 - 4x + 2

A school is organizing a fundraiser and the profit can be modeled by the polynomial P(x) = -2x^2 + 12x - 16, where x is the number of items sold. How many items must be sold to maximize profit?

• 5

• 3

• 10

• 1

A car's speed can be modeled by the polynomial S(t) = 4t^2 - 20t + 25, where t is the time in hours. What is the speed of the car at t = 2 hours?

• 1

• 10

• 15

• 5

A company produces a product and its cost function is given by C(x) = 3x^3 - 12x^2 + 9x + 5. Use the Remainder Theorem to find the cost when 2 units are produced.

• -1

• -3

• 0

• 5

A rectangular garden has a length of (x + 5) and a width of (x - 3). Write the polynomial expression for the perimeter of the garden and simplify it.

• 4x + 8

• 2x + 4

• 6x - 12

• 4x + 4

The height of a water tank is modeled by the polynomial H(x) = x^2 - 4x + 4. If the tank is filled to a height of 2 meters, what is the value of x?

• 1 ± √2

• 3 ± √2

• 2 + √3

• 2 ± √2

A local bakery sells cupcakes, and the revenue can be modeled by R(x) = x^3 - 6x^2 + 9x. What is the revenue when 3 cupcakes are sold?

• 3

• 9

• 0

• -3

A student is studying the polynomial function f(x) = x^4 - 2x^3 + x^2 - 5. Use the Remainder Theorem to find f(1).

• -5

• 0

• -6

• -4

A rectangular swimming pool has a length of (2x + 3) and a width of (x - 1). Write the polynomial expression for the area of the pool and evaluate it when x = 2.

• 7

• 5

• 10

• 8