Sure! Let's simplify the given expression step-by-step.
We start with the given expression:
[tex]\[
(x + 2)^2 - 3(x + 2) - 4
\][/tex]
Step 1: Expand [tex]\((x + 2)^2\)[/tex]
First, let's expand the squared term:
[tex]\[
(x + 2)^2 = x^2 + 4x + 4
\][/tex]
Step 2: Distribute [tex]\(-3\)[/tex] over [tex]\((x + 2)\)[/tex]
Next, distribute [tex]\(-3\)[/tex] over the term [tex]\((x + 2)\)[/tex]:
[tex]\[
-3(x + 2) = -3x - 6
\][/tex]
Step 3: Substitute the expanded terms back into the expression
Now we substitute these expanded terms back into the original expression:
[tex]\[
(x^2 + 4x + 4) - (3x + 6) - 4
\][/tex]
Step 4: Combine like terms
Now, let's combine the like terms:
[tex]\[
x^2 + 4x + 4 - 3x - 6 - 4
\][/tex]
Combine the [tex]\( x \)[/tex]-terms:
[tex]\[
x^2 + (4x - 3x) = x^2 + x
\][/tex]
Combine the constant terms:
[tex]\[
4 - 6 - 4 = -6
\][/tex]
Final simplified polynomial:
Putting it all together, we get:
[tex]\[
x^2 + x - 6
\][/tex]
So, the expression simplified to a polynomial is:
[tex]\[
x^2 + x - 6
\][/tex]
