Question

complete the factored form.
$x^2 + 22x + 121 = (x + 11)(x \underline{\quad})$
$x^2 + 22x + 121 = (x + 11)(x \boxed{\boldsymbol{\triangle}} \boxed{\quad})$

Explanation:

Step1: Recall perfect square formula

The perfect square trinomial formula is \( (a + b)^2 = a^2 + 2ab + b^2 \), or factored as \( (a + b)(a + b) \). For \( x^2 + 22x + 121 \), we identify \( a = x \), and \( 2ab = 22x \). Since \( a = x \), then \( 2xb = 22x \), so \( b = 11 \) (dividing both sides by \( 2x \)). Also, \( b^2 = 121 \), which matches \( 11^2 = 121 \).

Step2: Apply factoring

Using the formula, \( x^2 + 22x + 121=(x + 11)(x + 11) \), so the missing term is \( + 11 \).

Answer:

\( + 11 \) (or the box should be filled with \( 11 \) when considering the binomial factor \( (x + 11) \))