Factoring Polynomials: Real-Life Applications for 9th Graders

A gardener has a rectangular plot of land with an area represented by the polynomial x^2 + 5x + 6. If the length of the plot is represented by (x + 2), what is the width of the plot?

• x + 4

• x + 1

• x + 5

• x + 3

A company produces a product with a profit represented by the polynomial 2x^2 + 8x - 10. If the number of units sold is represented by (x - 1), use synthetic division to find the profit when 1 unit is sold.

• 0

• 15

• 5

• -10

A rectangular swimming pool has a length represented by the polynomial x^2 - 9. If the width is represented by (x - 3), what is the area of the pool?

• x^2 - 6x + 27

• x^3 - 9x + 9

• x^2 - 12

• x^3 - 3x^2 - 9x + 27

A farmer has a field with a total area represented by the polynomial 3x^2 + 12x. If he plants corn in rows represented by (3x), how many rows of corn can he plant?

• 3x + 4

• x^2 + 12

• 2x + 6

• x + 4

A school is organizing a play, and the total cost is represented by the polynomial x^2 + 4x - 5. If the ticket price is represented by (x - 1), how much profit will the school make if they sell 5 tickets?

• -x^2 + 5

• -x^2 + x

• 5x - 1

• x^2 + 4x + 5

A rectangular garden has a length represented by the polynomial x^2 + 3x - 4. If the width is represented by (x + 4), what is the area of the garden?

• x^3 + 7x^2 + 8x - 16

• x^2 + 7x - 4

• x^3 + 3x^2 + 12x

• x^3 + 4x^2 - 16

A toy company has a revenue represented by the polynomial 4x^2 - 16x. If they sell toys at a price represented by (2x), how many toys do they need to sell to break even?

• 2x + 4

• 4x - 16

• x - 8

• 2x - 8

A rectangular box has a volume represented by the polynomial x^3 - 4x^2 + 4x. If the height is represented by (x), what is the area of the base of the box?

• (x + 2)^2

• x^2 - 4

• (x - 2)^2

• x^3 - 4x

A car rental company has a profit represented by the polynomial 5x^2 - 20x. If they rent cars at a rate represented by (5x), how many cars do they need to rent to achieve a profit of $0?

• 8

• 6

• 4

• 2

A construction company has a project cost represented by the polynomial x^2 - 6x + 8. If they can reduce costs by factoring out (x - 2), what will be the new cost expression?

• x - 2

• x - 4

• x - 6

• x + 4