Question

which expression is equivalent to $n^2 + 26n + 88$ for all values of $n$?
\bigcirc $(n + 8)(n + 11)$
\bigcirc $(n + 4)(n + 22)$
\bigcirc $(n + 4)(n + 24)$
\bigcirc $(n + 8)(n + 18)$

Explanation:

Step1: Recall factoring trinomials

To factor \(n^2 + 26n + 88\), we need two numbers that multiply to \(88\) and add up to \(26\).

Step2: Find the two numbers

Factor pairs of \(88\): \(1\) & \(88\), \(2\) & \(44\), \(4\) & \(22\), \(8\) & \(11\).
Check which pair adds to \(26\): \(4 + 22 = 26\).

Step3: Write the factored form

So, \(n^2 + 26n + 88=(n + 4)(n + 22)\).

Answer:

B. \((n + 4)(n + 22)\)