The area of a rectangular art studio is given by the trinomial 24x2 – 4x – 8. What are the possible dimensions of the studio? Use factoring.

4(6x^2-x-2)

4(3x+2)(x-1)

whats funny?

exactly

This isn't the right answer. It's 2 sets, not this.

To find the possible dimensions of the studio, we need to factor the given trinomial, 24x^2 - 4x - 8.

To factor a trinomial, we look for two binomials whose product is equal to the given trinomial. In this case, we have:
24x^2 - 4x - 8 = ( )( )

First, we can look for the greatest common factor (GCF) of the three terms. The GCF of 24x^2, -4x, and -8 is 4. Factoring out the GCF, we have:
4(6x^2 - x - 2)

Now we have a quadratic trinomial inside the parentheses: 6x^2 - x - 2.

To factor the quadratic trinomial, we need to find two numbers whose product is equal to the product of the first and last coefficients (6 * -2 = -12), and whose sum is equal to the coefficient of the middle term (-1).

The numbers that satisfy these conditions are -4 and 3, because -4 * 3 = -12 and -4 + 3 = -1.

Now we can rewrite the quadratic trinomial as a product of two binomials:
6x^2 - x - 2 = (2x + 3)(3x - 2)

Therefore, the factored form of the original trinomial is:
24x^2 - 4x - 8 = 4(2x + 3)(3x - 2)

Now, let's look at the possible dimensions of the studio based on the factored form.

The width of the studio can be represented by (2x + 3), and the length can be represented by (3x - 2).

For the width, (2x + 3), we can set it equal to zero and solve for x:
2x + 3 = 0
2x = -3
x = -3/2

For the length, (3x - 2), we can set it equal to zero and solve for x:
3x - 2 = 0
3x = 2
x = 2/3

Therefore, the possible dimensions of the studio are:
Width: 2x + 3 = 2(-3/2) + 3 = -3 + 3 = 0
Length: 3x - 2 = 3(2/3) - 2 = 2 - 2 = 0

So, the possible dimensions of the studio are a width of 0 and a length of 0.