Mastering Polynomial Word Problems: Factoring & Grouping

A farmer has a rectangular field with a length of (3x + 6) meters and a width of (2x + 4) meters. What is the area of the field expressed as a polynomial?

• 6x^2 + 20x + 24

• 6x^2 + 24x + 24

• 5x^2 + 18x + 12

• 4x^2 + 16x + 30

A school is organizing a play and needs to arrange seats in rows. If the total number of seats is represented by the polynomial (x^2 + 5x + 6), how can the seats be grouped into rows of (x + 2) seats each?

• x + 3

• x + 1

• x + 4

• x + 5

A rectangular garden has a length of (x^2 + 3x) meters and a width of (x + 2) meters. Factor the polynomial to find the area of the garden.

• x^2 + 5x + 6

• (x + 3)(x + 2)

• x(x + 3)(x + 2)

• (x^2 + 5)(x - 1)

A box is designed such that its volume is represented by the polynomial (x^3 + 4x^2 + 4x). If the height of the box is (x + 2), what is the polynomial expression for the base area of the box?

• x^3 + 2x

• 4x^2 + 4

• x^2 + 4x

• x^2 + 2x

A company produces two types of gadgets. The total production can be represented by the polynomial (2x^2 + 8x). If they produce (2x) gadgets of the first type, how many gadgets of the second type do they produce?

• (2x^2 + 4x)

• (2x^2 + 10x)

• (2x^2 + 6x)

• (2x^2 + 8)

A rectangular swimming pool has a length of (x^2 + 2x) meters and a width of (x + 3) meters. What is the polynomial expression for the perimeter of the pool?

• 2x^2 + 4x + 3

• 2x^2 + 6x + 6

• 2x^2 + 8x + 12

• x^2 + 5x + 6

A recipe requires (x^2 + 5x + 6) cups of flour. If you use (x + 2) cups for one batch, how can you express the remaining flour as a polynomial?

• x^2 + 3x + 2

• x^2 + 4x + 4

• x^2 + 5x + 5

• x^2 + 6x + 6

A car rental company charges a flat fee of (3x + 15) dollars plus (2x) dollars per day. Write a polynomial to represent the total cost for x days of rental.

• 2x^2 + 3x + 15

• 2x^2 + 15

• 2x + 15

• 3x + 15

A rectangular plot of land has a length of (4x + 8) meters and a width of (2x + 4) meters. What is the polynomial expression for the area of the plot?

• 4x^2 + 16x + 16

• 10x^2 + 40x + 40

• 6x^2 + 24x + 24

• 8x^2 + 32x + 32

A local bakery sells cookies in boxes. If the total number of cookies is represented by the polynomial (x^2 + 4x + 4) and each box contains (x + 2) cookies, how many boxes can be filled?

• x + 2

• x + 1

• x + 3

• x + 4