Question

factor.
x^{2}+9x + 18

Explanation:

Step1: Find two numbers

We need two numbers that multiply to 18 and add up to 9. The numbers are 6 and 3 since $6\times3 = 18$ and $6 + 3=9$.

Step2: Rewrite the middle - term

Rewrite $9x$ as $6x+3x$. So, $x^{2}+9x + 18=x^{2}+6x+3x + 18$.

Step3: Group the terms

Group the terms: $(x^{2}+6x)+(3x + 18)$.

Step4: Factor out the GCF from each group

Factor out the GCF from each group. From $x^{2}+6x$, the GCF is $x$, so we get $x(x + 6)$. From $3x+18$, the GCF is 3, so we get $3(x + 6)$.

Step5: Factor out the common binomial factor

We have $x(x + 6)+3(x + 6)=(x + 3)(x+6)$.

Answer:

$(x + 3)(x + 6)$