The area of a rectangular classroom is given by the trinomial 10x^2 + 3x - 4. What are the possible dimensions of the classroom? Use factoring.
(1 point)
A. (5x - 4) and (2x + 1)
B. (5x - 4) and (2x - 1)
C. (5x + 4) and (2x - 1)
D. (5x + 4) and (2x + 1)
To find the possible dimensions of the classroom, we need to factor the trinomial 10x^2 + 3x - 4.
First, we can look for two numbers whose product is -40 (the product of the coefficient of x^2 and the constant term) and whose sum is 3 (the coefficient of x).
The numbers that satisfy these conditions are 8 and -5.
Now, we can rewrite the trinomial as:
10x^2 + 8x - 5x - 4
Next, we can factor by grouping:
(10x^2 + 8x) - (5x + 4)
2x(5x + 4) - 1(5x + 4)
Now, we can factor out the common binomial (5x + 4):
(5x + 4)(2x - 1)
Therefore, the possible dimensions of the classroom are (5x + 4) and (2x - 1).
The answer is C. (5x + 4) and (2x - 1).