Initial Knowledge Check

Rewrite the expression by factoring out $(x+2)$.
\[
3 x^{2}(x+2)-7(x+2)
\]

Step 1 ：Rewrite the expression by factoring out \((x+2)\) from the expression \(3 x^{2}(x+2)-7(x+2)\).

Step 2 ：This means we need to rewrite the expression in a form where \((x+2)\) is a common factor.

Step 3 ：To do this, we can simply write \((x+2)\) once and then write the remaining terms in parentheses. The remaining terms are obtained by dividing each term in the original expression by \((x+2)\).

Step 4 ：In this case, the remaining terms are \(3x^2\) and \(-7\). So, the factored form of the expression should be \((x+2)(3x^2 - 7)\).

Step 5 ：Let's verify this by expanding the factored form and check if it equals the original expression.

Step 6 ：The expanded factored expression equals the original expression. This means that the factored form of the expression is indeed \((x+2)(3x^2 - 7)\).

Step 7 ：Final Answer: The factored form of the expression \(3 x^{2}(x+2)-7(x+2)\) is \(\boxed{(x+2)(3x^2 - 7)}\).