The area of a rectangular room is given by the trinomial x2 – 3x – 28. What are the possible dimensions of the rectangle? Use factoring.
It’s (x+7) and (x-4)
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I know it’s (x+7) and (x-4), but can someone please explain why it isn’t (x-7) and (x+4)?
To find the possible dimensions of the rectangle, we need to factor the trinomial x^2 - 3x - 28.
First, we look for two numbers that multiply to -28 and add up to -3 (the coefficient of x). These numbers are -7 and 4, since (-7) * 4 = -28 and (-7) + 4 = -3.
Now, we can rewrite the trinomial as the product of two binomials:
x^2 - 7x + 4x - 28
Next, we group the terms:
(x^2 - 7x) + (4x - 28)
Now, we can factor out the greatest common factor from each group:
x(x - 7) + 4(x - 7)
We can see that we have a common binomial factor, which is (x - 7). Factoring out this binomial, we get:
(x - 7)(x + 4)
Therefore, the factored form of the trinomial x^2 - 3x - 28 is (x - 7)(x + 4).
From this, we can determine the possible dimensions of the rectangle. The length (L) of the rectangle corresponds to the binomial (x - 7), and the width (W) corresponds to the binomial (x + 4).
So, the possible dimensions of the rectangle are:
Length (L) = x - 7
Width (W) = x + 4
Note that this means the length must be greater than the width, since (x - 7) represents the length and (x + 4) represents the width.