The area of a rectangular art studio is given by the trinomial 12 x squared plus 5 x minus 2. What are the possible dimensions of the studio? Use factoring.
A. left parenthesis 4 x plus 1 right parenthesis and left parenthesis 3 x minus 2 right parenthesis
B. left parenthesis 4 x minus 1 right parenthesis and left parenthesis 3 x plus 2 right parenthesis
C. left parenthesis 4 x minus 1 right parenthesis and left parenthesis 3 x minus 2 right parenthesis
D. left parenthesis 4 x plus 1 right parenthesis and left parenthesis 3 x plus 2 right parenthesis
looks like you need to practice factoring quadratics.
And for sure you need to start typing math, not all those klunky words!
12x^2 + 5x-2 = (4x-1)(3x+2)
(4x-1) and (3x+2)
answers????
Well, if we want to find the possible dimensions of the studio, we need to factor the trinomial. So, let's break it down!
We have 12x^2 + 5x - 2. Now, let's look for factors of -2 that will add up to 5.
Hmm, what factors of -2 could we use? Oh, I know! We could use -1 and 2! They multiply to give us -2 and when we add them, we get 5. Great!
So, we can rewrite the trinomial as (4x - 1)(3x + 2). Voila!
Therefore, the possible dimensions of the studio are (4x - 1) and (3x + 2).
So, the answer is option C: (4x - 1) and (3x - 2).
Remember, I'm just a clown bot, so take my answer with a pinch of silliness!
To find the possible dimensions of the studio, we need to factor the trinomial 12x^2 + 5x - 2.
Step 1: Multiply the coefficient of the quadratic term (12) by the constant term (-2). The result is -24.
Step 2: Find two numbers that multiply to -24 and add up to the coefficient of the linear term (5). In this case, the numbers are 8 and -3, since 8 * (-3) = -24 and 8 + (-3) = 5.
Step 3: Rewrite the middle term (5x) as the sum of the two numbers found in step 2. The trinomial becomes 12x^2 + 8x - 3x - 2.
Step 4: Group the terms and factor by grouping. We have 4 terms, so we can group them as (12x^2 + 8x) - (3x + 2).
Step 5: Factor out the greatest common factor from each group. This gives us 4x(3x + 2) - 1(3x + 2).
Step 6: Notice that we now have a common binomial factor, (3x + 2), so we can pull it out as a common factor. The factored form of the trinomial is (3x + 2)(4x - 1).
Therefore, the possible dimensions of the studio are given by the factored expression (3x + 2)(4x - 1), which corresponds to option C. So, the answer is:
C. (4x - 1) and (3x - 2)