Factoring Polynomials and Finding Roots in Real-World Scenarios

A gardener is planting a rectangular flower bed. The area of the bed can be represented by the polynomial A(x) = x^2 - 9. What are the dimensions of the flower bed if the width is x - 3?

• Width: x - 3, Length: x - 3

• Width: x + 3, Length: x - 3

• Width: x - 3, Length: x + 3

• Width: x + 3, Length: x + 3

A car's speed can be modeled by the polynomial S(t) = t^2 - 4t. What are the times when the car is stationary?

• t = 0, t = 4

• t = 1

• t = -4

• t = 2

A rectangular pool has a length represented by the polynomial L(x) = x^2 - 16. If the width is x - 4, what are the possible dimensions of the pool?

• (x^2 - 16, x - 4)

• (x^2 - 8, x + 2)

• (x^2 - 4, x - 2)

• (x^2 + 16, x + 4)

A company produces x^2 - 25 units of a product. If they want to factor this polynomial to find the number of units produced, what are the factors?

• (x - 1)(x + 25)

• (x - 5)(x - 5)

• (x - 10)(x + 10)

• (x - 5)(x + 5)

A rectangular garden has an area represented by the polynomial A(x) = x^2 - 1. If one side is x + 1, what is the length of the other side?

• x - 1

• x + 1

• x - 2

• x^2 + 1

A box's volume is given by the polynomial V(x) = x^3 - 8. If one dimension is x - 2, what are the possible dimensions of the box?

• x + 2

• x^3 - 2

• x^2 - 4

• x - 2, x^2 + 2x + 4 (complex dimensions)

A farmer has a field with an area represented by the polynomial A(x) = x^2 - 36. If the length is x + 6, what is the width of the field?

• x + 12

• x + 6

• x - 6

• x - 12

A school is organizing a play and the seating arrangement can be represented by the polynomial S(n) = n^2 - 9n. What are the values of n when there are no seats left?

• 4, 5

• 0, 9

• 1, 8

• 3, 6

A rectangular plot of land has an area represented by the polynomial A(x) = x^2 - 25. If the length is x + 5, what is the width of the plot?

• x + 10

• x - 10

• x - 5

• x + 5

A toy manufacturer has a production model represented by the polynomial P(x) = x^2 - 4. What are the roots of this polynomial, indicating the production levels where the output is zero?

• 1, -1

• 3, -3

• 0, 4

• 2, -2