Certainly! Let's work through the expression step-by-step to find its equivalent form.
We begin with the given expression:
[tex]\[ -3x^2 - 24x - 36 \][/tex]
Step 1: Factor out the common factor.
Notice that each term has a common factor of -3. Factoring -3 out from the expression, we get:
[tex]\[ -3(x^2 + 8x + 12) \][/tex]
Step 2: Factor the quadratic expression inside the parentheses.
Next, we need to factor [tex]\( x^2 + 8x + 12 \)[/tex]. To do this, we look for two numbers that multiply to 12 (the constant term) and add up to 8 (the coefficient of the linear term). These numbers are 2 and 6.
So, we can write the quadratic expression as a product of two binomials:
[tex]\[ x^2 + 8x + 12 = (x + 2)(x + 6) \][/tex]
Step 3: Combine the factored terms.
Substitute the factored quadratic back into the expression with the common factor:
[tex]\[ -3(x^2 + 8x + 12) = -3(x + 2)(x + 6) \][/tex]
Thus, the equivalent expression is:
[tex]\[ -3(x + 2)(x + 6) \][/tex]
Therefore, we have:
\[tex]$
-3 (x + 2) (x + 6)
\$[/tex]
So, the correct selections for the drop-down menus are:
\[tex]$
-3(x + 2)(x + 6)
\$[/tex]
Make sure to select -3 for the first box, 2 for the second box, and 6 for the third box.
