Solve:
$P (x) = x^{2} + 5 x + 6$

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Solution

In the given polynomial $x^{2} + 5 x + 6$ ,
The first term is $x^{2}$ and its coefficient is $1$ .
The middle term is $5 x$ and its coefficient is $5$ .
The last term is a constant term $6$ .

Multiply the coefficient of the first term by the constant $1 \times (6) = 6$ .

We now find the factor of $6$ whose sum equals the coefficient of the middle term, which is $5$ and then factorize the polynomial $x^{2} + 5 x + 6$ as shown below:
$x^{2} + 5 x + 6 = x^{2} + 2 x + 3 x + 6 = x (x + 2) + 3 (x + 2) = (x + 2) (x + 3)$

Hence, $x^{2} + 5 x + 6 = (x + 2) (x + 3)$ .

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