Question

Factorise $x^{2}+9 x+18$

Answer 1

The given expression is $x^{2}+9 x+18$.

We try to split 9 into two parts whose sum is 9 and product 18 .

Clearly, $6+3=9$ and $6 \times 3=18$.

$$

\begin{aligned}

\therefore \quad x^{2}+9 x+18 &=x^{2}+6 x+3 x+18 \\

&=x(x+6)+3(x+6) \\

&=(x+6)(x+3) .

\end{aligned}

$$

Hence, $x^{2}+9 x+18=(x \div 6)(x+3)$.