Adding Polynomials

Abigail is trying to calculate the total volume of two different boxes. The volume of the first box is represented by the polynomial (x³-6x²+3) and the volume of the second box is represented by the polynomial (3x³+4x-1). What is the total volume of the two boxes?

• 4x³-2x²+2

• 4x³-6x²+4x+2

• -2x³+2x+2

• 4x³-2x²-2

• None of these

Abigail is designing a garden and wants to classify the expression for the area of a section of the garden: 3x² – 8x + 1

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

• Constant

Ethan is trying to simplify the expression for his math homework.

(4a³ - 8a - 4a²) + (7a³ - 7 - 6a)

• 11a³ - 4a² - 14a - 7

• 5a³ - 4a² - 14a - 7

• 5a³ - 4a² - 20a - 7

• 5a³ - 9a² - 20a - 7

Benjamin is calculating the total cost of two different sets of items he wants to buy. The cost of the first set is represented by (3y² + y³ - 5) dollars, and the cost of the second set is represented by (4y² -4y + 2y³ + 8) dollars. What is the total cost?

• 3y³ + 7y² - 4y + 3

• 4y² + 3y³ - y + 3

• -y⁴ + 2y³ -y - 4

• 4y³ + 3y² -3y + 1

• None of these

Ethan is trying to categorize the expression he found in his math book:

3xy + 4x + 5y + 6

• monomial

• binomial

• trinomial

• polynomial

• Constant

Hannah is organizing a math competition and she writes the following polynomial on the board in standard form:
7x³ - 11x² + 8x - 5. Is this statement true?

• True

• False

(2x + 5y - z) + (-6x - 4y + 7z)

• -4x +6y + 6z

• 4x + y + 6z

• -4x - y + 6z

• -4x + y + 6z

• None of these

Ava and Emma are working on a project together. Ava contributes (4x³-5x²+3x) hours, while Emma contributes (-2x³-x²+6x) hours. How many hours did they work on the project in total?

• 2x³-6x²-9x

• 2x³+6x²+9x

• -2x³-6x²+9x

• 2x³-6x²+9x

• None of these

Abigail is organizing her books and wants to simplify the arrangement. She has (4a³ - 8a - 4a²) books on one shelf and (7a³ - 7 - 6a) books on another shelf. Help her simplify the total number of books.

• 11a³ - 4a² - 14a - 7

• 5a³ - 4a² - 14a - 7

• 5a³ - 4a² - 20a - 7

• 5a³ - 9a² - 20a - 7

Daniel is calculating the total area of two rectangular fields. The area of the first field is represented by (6x² + 3x - 2) square meters, and the area of the second field is represented by (4x² - 5x + 7) square meters. What is the total area?

• 10x² - 8x + 5

• 10x² - 2x + 5

• 10x² - 2x + 9

• 10x² + 2x + 5