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.
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.
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)