Real-Life Polynomial Division: Remainders & Factoring Fun

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 plots can he create, and what is the remainder?

• 1 plot, remainder 1

• 3 plots, remainder 2

• 2 plots, remainder 1

• 1 plot, remainder 0

A school is organizing a fundraiser and has raised money represented by the polynomial 2x^2 + 8x + 6. If they want to divide this amount equally among x + 3 students, how much does each student get, and is there any remainder?

• Each student gets 2x + 1 with no remainder.

• Each student gets 2x + 3 with a remainder of 2.

• Each student gets 2x + 4 with a remainder of 6.

• Each student gets 2x + 2 with no remainder.

A company produces a product represented by the polynomial 3x^3 + 12x^2 + 12x. If they want to package it in boxes that can hold x + 2 items each, how many boxes will they need, and what will be left over?

• 3x^2 + 6x boxes, 0 left over

• 3x^2 + 3x boxes, 3 left over

• 4x^2 + 8x boxes, 2 left over

• 2x^2 + 4x boxes, 1 left over

A gardener has a flower bed represented by the polynomial x^2 - 4. If he wants to divide it into sections of x - 2, how many sections can he create, and is there any remainder?

• 1 section, no remainder

• 3 sections, no remainder

• 1 section, with remainder 2

• 2 sections, no remainder

A bookstore has a collection of books represented by the polynomial 4x^2 + 8x + 4. If they want to arrange them in groups of 2x + 2, how many groups can they form, and what is the remainder?

• 2 groups, remainder 0

• 1 group, remainder 2

• 3 groups, remainder 1

• 4 groups, remainder 0

A local bakery has a batch of cookies represented by the polynomial x^3 + 3x^2 + 3x + 1. If they want to package them in boxes of x + 1 cookies each, how many boxes can they fill, and is there any remainder?

• 3 boxes, no remainder

• 2 boxes, 1 cookie remainder

• 1 box, 2 cookies remainder

• 1 box, no remainder

A construction company has a project represented by the polynomial 5x^2 + 10x + 5. If they want to divide the work among teams represented by x + 1, how many teams can they form, and what is the remainder?

• 4 teams with a remainder of 1

• 5 teams with a remainder of 0

• 5 teams with a remainder of 3

• 6 teams with a remainder of 2

A charity event has donations represented by the polynomial 6x^3 + 9x^2 + 3x. If they want to distribute these donations equally among x + 1 recipients, how much does each recipient get, and is there any remainder?

• 3x + 9, remainder 3

• 6x^2 + 3x, remainder 0

• 6x^3 + 9x^2, remainder 0

• 6x^2 + 3x, remainder 1

A car rental service has a fleet represented by the polynomial 2x^2 + 4x. If they want to divide the cars into groups of x + 2, how many groups can they create, and what is the remainder?

• 3x groups, remainder 1

• 2x groups, remainder 0

• x groups, remainder 2

• 4x groups, remainder 0

A tech company has a software represented by the polynomial x^3 - 1. If they want to divide it into modules represented by x - 1, how many modules can they create, and is there any remainder?

• 1 module, no remainder

• 2 modules, no remainder

• 3 modules, no remainder

• 1 module, with a remainder of 1