Real-World Polynomial Division: Engage with Synthetic Division

A farmer has a rectangular field represented by the polynomial x^2 + 5x + 6. He wants to divide it into smaller plots, each represented by the polynomial x + 2. How many smaller plots can he create?

• x + 4

• x + 1

• x + 3

• x + 5

A school is organizing a fundraiser and has raised money represented by the polynomial 2x^2 + 8x + 10. If they want to divide this amount equally among x + 5 students, how much will each student receive?

• 2x + 5

• x + 2

• 2x + 2

• 2x + 1

A company produces a product represented by the polynomial 3x^3 + 12x^2 + 9x. If they want to package it in boxes represented by the polynomial 3x + 3, how many boxes can they fill?

• x^2 + 3x

• 3x^2 + 9

• x^3 + 4x^2 + 3

• x^2 + 3

A recipe calls for a mixture represented by the polynomial 4x^2 + 16x + 15. If the mixture is to be divided into portions represented by the polynomial 2x + 3, how many portions can be made?

• 2x + 4

• 2x + 6

• 2x + 5

• 4x + 3

A car rental service has a fleet represented by the polynomial x^3 + 3x^2 + 4x. If they want to divide the cars into groups represented by the polynomial x + 1, how many groups can they form?

• 1

• 2

• 4

• 3

A gardener has a flower bed represented by the polynomial 5x^2 + 20x + 15. If he wants to divide it into sections represented by the polynomial 5x + 5, how many sections will he have?

• 4

• 3

• 2

• 5

A bookstore has a collection of books represented by the polynomial 6x^3 + 18x^2 + 12x. If they want to arrange them in stacks represented by the polynomial 6x + 6, how many stacks can they create?

• x(x + 2)

• 6(x + 1)

• 3(x^2 + 2x)

• 2x(x + 3)

A construction company has a project represented by the polynomial 7x^2 + 14x + 7. If they want to divide the project into tasks represented by the polynomial 7, how many tasks will there be?

• 4

• 2

• 1

• 3

A bakery has a batch of cookies represented by the polynomial 8x^2 + 32x + 32. If they want to package them in boxes represented by the polynomial 8x + 8, how many boxes can they fill?

• (x + 3) with a remainder of 1 when x = -1

• (x + 1) with a remainder of 0 when x = 0

• (x + 4) with a remainder of 0 when x = -2

• (x + 2) with a remainder of 0 when x = -1

A tech company has a software represented by the polynomial 9x^3 + 27x^2 + 18x. If they want to distribute it among teams represented by the polynomial 9x + 9, how many teams will receive it?

• 2

• 4

• 3

• 1