Factoring Trinomials: Real-Life Applications & Strategies

A rectangular garden has an area represented by the trinomial x^2 + 5x + 6. What are the dimensions of the garden?

• x + 5 and x + 1

• x + 2 and x + 3

• x + 4 and x + 2

• x + 1 and x + 6

A box is designed such that its volume can be expressed as the trinomial x^3 + 3x^2 + 2x. If the height of the box is x, what is the area of the base?

• x^3 + 2x + 1

• x^2 + 2x + 3

• x^2 + 3x + 2

• 3x^2 + 2x + 1

The area of a triangular plot of land is given by the trinomial 2x^2 + 8x + 6. Factor this expression to find the base and height of the triangle.

• Base: (2x + 3), Height: (x + 2)

• Base: (x + 1), Height: (x + 3)

• Base: (x + 2), Height: (x + 4)

• Base: (x + 5), Height: (x + 1)

A company produces a product with a profit represented by the trinomial 3x^2 + 12x + 12. What factors can be used to determine the number of units sold for maximum profit?

• 3(x + 4)(x + 1)

• 3(x + 2)^2

• (x + 3)(3x + 4)

• (3x + 6)(x + 2)

A farmer wants to fence a rectangular field with an area of x^2 + 7x + 10. What are the possible lengths and widths of the field?

• (x + 3) and (x + 4)

• (x + 6) and (x + 2)

• Possible lengths and widths are (x + 2) and (x + 5).

• (x + 1) and (x + 10)

The area of a painting is represented by the trinomial x^2 - 9. What are the dimensions of the painting if it can be factored?

• (x - 1) and (x + 1)

• (x - 2) and (x + 5)

• (x - 4) and (x + 4)

• (x - 3) and (x + 3)

Tags

CCSS.HSA-REI.B.4B

A school is planning a rectangular playground with an area of x^2 + 4x - 5. What are the possible dimensions of the playground?

• (x + 5) and (x - 1)

• (x + 1) and (x - 5)

• (x + 4) and (x - 2)

• (x + 3) and (x - 3)

A rectangular swimming pool has an area of 4x^2 + 12x + 9. Factor this expression to find the dimensions of the pool.

• (2x + 1) by (2x + 9)

• (x + 6) by (4x - 3)

• (2x + 3) by (2x + 3)

• (4x + 3) by (x + 3)

A local business has a revenue represented by the trinomial x^2 + 6x + 8. What factors can help determine the pricing strategy?

• (x + 1)(x + 8)

• (x + 3)(x + 5)

• (x + 2)(x + 6)

• (x + 2)(x + 4)

A rectangular plot of land has an area of 5x^2 + 20x + 15. Factor this expression to find the possible dimensions of the plot.

• 5(x + 2)(x + 3)

• (x + 5)(5x + 3)

• 5(x + 1)(x + 3)

• (5x + 15)(x + 1)