Real Life Polynomial Differences: Word Problems for Grade 8

A gardener has a polynomial expression for the area of a flower bed given by A(x) = 3x^2 + 5x - 2. After removing a section of the bed, the new area is represented by B(x) = 2x^2 + 3x - 4. What is the polynomial expression for the area of the removed section?

• x^2 + 4x - 1

• 2x^2 + 5x - 2

• 3x^2 + 3x - 4

• x^2 + 2x + 2

A school is planning to build a new playground. The area of the playground is represented by P(x) = 4x^2 + 6x - 10. If they decide to reduce the area by a section represented by R(x) = 2x^2 + 4x - 5, what is the new area of the playground?

• 2x^2 + 2x - 5

• 2x^2 + 6x - 5

• 4x^2 + 6x - 10

• 2x^2 + 4x - 5

A farmer has a field represented by the polynomial F(x) = 5x^2 + 3x - 7. After selling a portion of the field, the remaining area is represented by S(x) = 3x^2 + 2x - 4. What is the polynomial expression for the area of the sold portion?

• 4x^2 + x - 5

• 5x^2 + 3x - 4

• 3x^2 + x - 2

• 2x^2 + x - 3

A company produces x^3 + 2x^2 - 5x units of a product. After a reduction in production, the new production level is represented by 2x^3 - 3x^2 + 4x. What is the polynomial that represents the decrease in production?

• -x^3 + 5x^2 - 9x

• x^3 - 5x^2 + 9x

• -2x^3 + 3x^2 - 4x

• 3x^3 - 2x^2 + 5x

A car rental service has a polynomial expression for their total revenue given by R(x) = 6x^2 + 4x - 20. If they have expenses represented by E(x) = 3x^2 + 2x - 10, what is the polynomial expression for their profit?

• 3x^2 + 2x + 10

• 6x^2 + 4x - 10

• 3x^2 + 2x - 10

• 9x^2 + 6x - 30

A bookstore has a polynomial expression for their inventory given by I(x) = 7x^2 + 5x - 15. After selling some books, the new inventory is represented by N(x) = 4x^2 + 3x - 10. What is the polynomial expression for the number of books sold?

• 4x^2 + 2x - 15

• 5x^2 + 3x - 10

• 3x^2 + 2x - 5

• 2x^2 + 2x - 5

A restaurant's monthly expenses are represented by the polynomial E(x) = 8x^2 + 6x - 30. If they manage to reduce their expenses to E'(x) = 5x^2 + 3x - 20, what is the polynomial expression for the amount they saved?

• 2x^2 + 2x - 5

• 6x^2 + 5x - 25

• 4x^2 + 4x - 15

• 3x^2 + 3x - 10

A construction company has a polynomial expression for the cost of a project given by C(x) = 10x^2 + 8x - 50. If they find a way to reduce costs represented by D(x) = 4x^2 + 2x - 20, what is the polynomial expression for the cost reduction?

• 7x^2 + 4x - 15

• 5x^2 + 10x - 25

• 8x^2 + 3x - 40

• 6x^2 + 6x - 30

A tech company has a polynomial expression for their revenue given by R(x) = 12x^2 + 10x - 40. If their expenses are represented by E(x) = 7x^2 + 5x - 25, what is the polynomial expression for their net revenue?

• 12x^2 + 15x - 65

• 6x^2 + 5x - 10

• 5x^2 + 5x - 15

• 5x^2 + 3x - 20

A local bakery has a polynomial expression for their daily sales given by S(x) = 9x^2 + 7x - 30. If they have a decrease in sales represented by D(x) = 5x^2 + 3x - 15, what is the polynomial expression for the decrease in sales?

• 5x^2 + 3x - 15

• 9x^2 + 7x - 15

• 6x^2 + 5x - 20

• 4x^2 + 2x - 10