The area of a rectangular pool is given by the trinomial 2y^2-y-3 . What are the possible dimensions of the pool? Use factoring.
To find the possible dimensions of the pool, we need to factor the trinomial 2y^2-y-3.
The factored form of the trinomial is:
2y^2-y-3 = (2y+3)(y-1)
So the possible dimensions of the pool are:
Length = 2y + 3
Width = y - 1
Therefore, the possible dimensions of the rectangular pool are:
Length = 2y + 3
Width = y - 1
a (-y-1) and (-2y-3)
b (y+1) and (2y-3)
c (2y-1) and (2y-3)
d (2y+1) and (y-3)
The correct answer is:
b) (y+1) and (2y-3)
can you explain?
Sure!
First, we find the factors of the trinomial 2y^2-y-3, which are (2y+3)(y-1).
From this, we can determine the possible dimensions of the rectangular pool:
- Length = 2y + 3
- Width = y - 1
However, when expressing the dimensions in terms of the factors, we need to ensure that the signs are appropriately included.
In the correct answer choice b):
- (y + 1) matches the (y - 1) factor, providing the width of the rectangular pool.
- (2y - 3) matches the (2y + 3) factor, providing the length of the rectangular pool.
Therefore, choice b) (y + 1) and (2y - 3) is the correct answer.