Sure, let's break down the given expression to identify an equivalent factored form.
The given expression is:
[tex]\[
-3x^2 - 24x - 36
\][/tex]
To begin, we look for common factors in each term of the quadratic expression. Observing that each term has a factor of [tex]\(-3\)[/tex], we can factor out [tex]\(-3\)[/tex] from the quadratic expression:
[tex]\[
-3(x^2 + 8x + 12)
\][/tex]
Next, we focus on factoring the quadratic expression inside the parentheses: [tex]\(x^2 + 8x + 12\)[/tex]. We want to find two numbers that add up to [tex]\(8\)[/tex] (the coefficient of [tex]\(x\)[/tex]) and multiply to [tex]\(12\)[/tex] (the constant term).
These two numbers are [tex]\(2\)[/tex] and [tex]\(6\)[/tex] because:
[tex]\[
2 + 6 = 8 \quad \text{and} \quad 2 \times 6 = 12
\][/tex]
Thus, we can factor [tex]\(x^2 + 8x + 12\)[/tex] as:
[tex]\[
(x + 2)(x + 6)
\][/tex]
Putting it all together, the entire factored form of the original expression becomes:
[tex]\[
-3(x + 2)(x + 6)
\][/tex]
So, inserting this into the original expression format given in the question, we have:
[tex]\[
-3(x + \square)(x + \square)
\][/tex]
Thus, the final correct expression is:
[tex]\[
-3 \, (x+2) \, (x+6)
\][/tex]
Make sure to select '2' and '6' in the corresponding drop-down menus.
