Verify the Factorization: x² + 3x - 18 = (x+6)(x-3)

Let's begin by factorizing the given expression using quick trinomial factoring:

$x^2+3x-18$

We'll look for a pair of numbers whose product is the free term in the expression, and whose sum is the coefficient of the first-degree term, meaning two numbers $m,\hspace{2pt}n$ that satisfy:

$m\cdot n=-18\\ m+n=3\\$From the first requirement mentioned, that is - from the multiplication, we should note that the product of the numbers we're looking for needs to yield a negative result. Therefore we can conclude that the two numbers have different signs, according to multiplication rules. The possible factors of 18 are 2 and 9, 6 and 3, or 18 and 1. Meeting the second requirement mentioned, along with the fact that the numbers we're looking for have different signs leads us to the conclusion that the only possibility for the two numbers we're looking for is:

$\begin{cases} m=6\\ n=-3 \end{cases}$

Therefore we'll factorize the given expression to:

$x^2+3x-18 \\ \downarrow\\ (x+6)(x-3)$

It is clear that the suggested factorization in the problem is correct.

Therefore - the correct answer is answer A.

Note:

The given question could also be solved by expanding the parentheses in the suggested expression:

$(x+6)(x-3)$(using the expanded distributive law), and checking if indeed we obtain the given expression:

$x^2+3x-18$, However it is of course preferable to try to factorize the given expression - for practice purposes.