Answer:
The possible dimensions of the park are (x + 7) and (x + 8) where x is any number
Step-by-step explanation:
If an area of a rectangle is A = ax² + bx + c, then the dimensions of the rectangle are the factors of ax² + bx + c
∵ A rectangular skateboard park has an area of x² + 15x + 56
∴ A = x² + 15x + 56
- Lets factorize the trinomial x² + 15x + 56 into two factors
∵ The last sign of it is (+)
∴ The two factors have the same middle sign
∵ The middle sign of it is (+)
∴ The two factors have (+) as a middle sign
∵ x² = x × x
∵ 56 = 7 × 8
∵ 7 × x + 8 × x = 15x ⇒ middle term
- That means the factors of x² + 15x + 56 are (x + 7) and (x + 8)
∴ The factors of x² + 15x + 56 are (x + 7) and (x + 8)
∵ A = x² + 15x + 56
∴ A = (x + 7)(x + 8)
∵ Area of the rectangle = The product of its dimensions
∴ (x + 7) and (x + 8) are the dimensions of the park
The possible dimensions of the park are (x + 7) and (x + 8) where x is any number
