8th Grade Polynomial Expressions & Equations Challenge

A gardener has 3x^2 + 5x + 2 flower plants in one section and 2x^2 + 3x + 4 in another. How many plants does he have in total?

• 6x^2 + 2x + 3

• 5x^2 + 8x + 6

• 4x^2 + 7x + 5

• 3x^2 + 5x + 4

A school is organizing a fundraiser. They raised 4x^2 + 6x + 5 dollars in the first week and 2x^2 + 3x + 7 dollars in the second week. How much money did they raise altogether?

• 4x^2 + 9x + 5

• 5x^2 + 8x + 10

• 7x^2 + 6x + 15

• 6x^2 + 9x + 12

A rectangular garden has a length of (x + 3) meters and a width of (2x + 1) meters. What is the area of the garden expressed as a polynomial?

• 2x^2 + 6x + 3

• 2x^2 + 7x + 3

• x^2 + 5x + 3

• 4x^2 + 9x + 1

If a box has a volume represented by the polynomial V = x^3 + 2x^2 - 5x, and you remove a smaller box with volume x^2 - 3x, what is the volume of the remaining box?

• x^2 - 2x + 5

• x^3 + x^2 - 2x

• x^3 + 2x^2 - 5x

• x^3 - 3x

A car travels a distance represented by the polynomial d = 5x^2 + 10x - 15 kilometers. If it travels back a distance of 3x^2 - 5x + 10 kilometers, what is the total distance traveled?

• 7x^2 + 5x - 10

• 10x^2 - 5x + 15

• 5x^2 + 15x - 5

• 8x^2 + 5x - 5

A factory produces x^3 - 4x^2 + 6x items in the first month and 2x^3 + 3x^2 - 2x in the second month. How many items did the factory produce in total?

• 2x^3 + 7x^2 - 2x

• 5x^3 - 4x^2 + 2x

• 3x^3 - x^2 + 4x

• x^3 + 2x^2 + 6x

A rectangle has a perimeter represented by the polynomial P = 2(x + 4) + 2(3x + 1). What is the simplified expression for the perimeter?

• 4x + 6

• 6x + 8

• 10x + 12

• 8x + 10

If the polynomial equation 2x^2 - 8 = 0 represents the height of a building, what are the possible heights of the building?

• -2

• 4

• 0

• 2

A farmer has a field represented by the polynomial A = x^2 + 5x + 6 acres. If he sells a portion of the field represented by x^2 - 2x, what is the area of the field he still owns?

• 7x + 6

• x^2 + 7x + 6

• x^2 + 3x + 6

• x^2 + 5x + 2

A company’s profit is represented by the polynomial P = 3x^2 + 12x - 9. If they lose a certain amount represented by the polynomial L = x^2 + 4x, what is the new profit expression?

• x^2 + 8x - 9

• 2x^2 + 4x - 9

• 3x^2 + 8x - 9

• 2x^2 + 8x - 9