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.

Answer 1

To find the possible dimensions of the classroom, we need to factor the trinomial expression.

First, we look for two numbers that multiply to -40 (the product of the constant term and the x^2 term) and add to the coefficient of the x term, which is 3.

After some trial and error, we find that the factors of -40 that satisfy this condition are 8 and -5, since 8 * -5 = -40 and 8 + (-5) = 3.

Next, we rewrite the original trinomial expression using these factors:
10x^2 + 3x - 4
= 10x^2 + 8x - 5x - 4

Now, we group the terms:
= (10x^2 + 8x) + (-5x - 4)

Then, we factor out the greatest common factor from each group:
= 2x(5x + 4) - 1(5x + 4)

Notice that we have a common binomial factor, (5x + 4), which we can then factor out:
= (2x - 1)(5x + 4)

Therefore, the factored form of the trinomial is (2x - 1)(5x + 4).

To find the possible dimensions of the classroom, we set each factor equal to zero and solve for x:
2x - 1 = 0 OR 5x + 4 = 0

For the first equation, adding 1 to both sides gives:
2x = 1

Dividing both sides by 2, we find:
x = 1/2

For the second equation, subtracting 4 from both sides gives:
5x = -4

Dividing both sides by 5, we find:
x = -4/5

So, the possible dimensions of the rectangular classroom are x = 1/2 and x = -4/5.

Answer 2

what if the possible answers are
1. (5x-4) and (2x+1)
2. (5x-4) and (2x-1)
3. (5x+4) and (2x-1)
4. (5x+4) and (2x+1)