Factoring and Distributing: Real-Life Expressions Quiz

A rectangular garden has a length of (x + 5) meters and a width of (x - 2) meters. What is the expression for the area of the garden in terms of x?

• x^2 - 3x - 10

• x^2 + 7x - 10

• x^2 + 3x - 10

• x^2 + 3x + 10

If the area of a square is represented by the expression (x^2 + 6x + 9), what is the length of one side of the square?

• x + 2

• x + 4

• x + 5

• x + 3

A box has a volume represented by the expression (x^3 + 3x^2 - 4x). If one dimension of the box is (x), what is the expression for the area of the base of the box?

• x^3 + 4x - 3

• 3x^2 - 4x + 1

• x^2 + 3x - 4

• x^2 - 3x + 4

A school is planning to build a new playground. The area of the playground is represented by the expression (2x^2 + 8x). If they want to factor this expression to find the dimensions, what are the factors?

• 2x(x + 4)

• (x + 2)(2x + 4)

• 4(2x + 2)

• x(2x + 8)

A farmer has a field that can be represented by the expression (x^2 - 9). If he wants to fence the field, what are the possible dimensions he can use?

• Dimensions: (x - 1) and (x + 1) for x > 1.

• Dimensions: (x - 2) and (x + 2) for x > 2.

• Dimensions: (x - 3) and (x + 3) for x > 3.

• Dimensions: (x - 4) and (x + 4) for x > 4.

The area of a triangular plot of land is given by the expression (3x^2 + 12x). If the height of the triangle is (3), what is the expression for the base of the triangle?

• (6x^2 + 12x)

• (2x^2 + 8x)

• (x^2 + 4x)

• (3x^2 + 4x)

A rectangular pool has a length represented by (x + 4) and a width represented by (x - 1). What is the expression for the perimeter of the pool?

• 4x + 6

• 3x + 5

• 4x + 8

• 2x + 6

A company produces a product with a profit represented by the expression (x^2 - 5x + 6). What are the factors of this profit expression?

• (x - 1)(x - 6)

• (x + 2)(x + 3)

• (x - 2)(x - 3)

• (x - 4)(x - 2)

A rectangular painting has a length of (2x + 3) and a width of (x - 1). What is the expression for the area of the painting?

• 4x + 2

• 2x^2 + x - 3

• x^2 + 5x - 3

• 2x^2 - x + 3

A local bakery sells cookies in boxes. The total number of cookies can be represented by the expression (x^2 + 5x). If each box holds (x) cookies, how many boxes can be filled?

• 5x

• x^2 + 5

• x + 5

• x^2 + 5x