Question

factor
$n^2 + 16n + 63$
$(n+7)(n+9)$
$(n-7)(n+4)$
$(n+7)(n-9)$
$(n-3)(n-10)$

Explanation:

Step1: Recall factoring trinomial

To factor \(n^2 + 16n + 63\), we need two numbers that multiply to \(63\) and add up to \(16\).

Step2: Find the numbers

The factors of \(63\) are: \(1\) & \(63\), \(3\) & \(21\), \(7\) & \(9\). Among these, \(7 + 9 = 16\).

Step3: Write the factored form

So, \(n^2 + 16n + 63=(n + 7)(n + 9)\) by using the formula \(x^2+(a + b)x+ab=(x + a)(x + b)\) where \(a = 7\) and \(b = 9\).

Answer:

A. \((n + 7)(n + 9)\)