The area of a rectangular classroom is given by the trinomial 10x2 + 3x – 4. What are the possible dimensions of the classroom? Use factoring.
To find the possible dimensions of the classroom, we need to factor the trinomial 10x^2 + 3x - 4.
We can start by looking for two numbers that multiply to give -40 (the product of 10 and -4) and add up to 3 (the coefficient of the middle term). The numbers 8 and -5 fit this criteria, as 8 * -5 = -40 and 8 + (-5) = 3.
Now, we can rewrite 10x^2 + 3x - 4 as the product of two binomials using these numbers:
10x^2 + 3x - 4 = (5x + 8)(2x - 5)
By the Zero Product Property, setting either factor equal to zero will give us one of the possible dimensions of the classroom. Thus, we have two possible dimensions:
1) 5x + 8 = 0
5x = -8
x = -8/5
So, one possible dimension is x = -8/5.
2) 2x - 5 = 0
2x = 5
x = 5/2
The other possible dimension is x = 5/2.
Therefore, the possible dimensions of the classroom are -8/5 and 5/2.