To factor the quadratic expression \(x^2 + 11x + 18\) into the product of two binomials, we will look for two numbers that multiply to \(18\) (the constant term) and add to \(11\) (the coefficient of the \(x\) term).
Considering the factors of \(18\):
- \(1\) and \(18\) (sum = \(19\))
- \(2\) and \(9\) (sum = \(11\))
- \(3\) and \(6\) (sum = \(9\))
The pair that adds up to \(11\) is \(2\) and \(9\). Therefore, we can write the expression as:
\[ x^2 + 11x + 18 = (x + 2)(x + 9) \]
Thus, the factored form of the quadratic is:
\[ \boxed{(x + 2)(x + 9)} \]
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