Verify the Factorization: x²+x-20 = (x+2)(x-10)

Let's ascertain whether the following expression can be factorized using quick trinomial factoring:

$x^2+x-20$

We'll begin by looking for a pair of numbers whose product is the free term in the expression, and whose sum is the coefficient of the first power term in the expression . Meaning two numbers $m,\hspace{2pt}n$ that satisfy the following expression:

$m\cdot n=-20\\ m+n=1\\$From the first requirement mentioned, namely - 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 the multiplication rules. The possible factors of 20 are 2 and 10, 4 and 5, or 20 and 1, fulfilling the second requirement mentioned, along with the fact that the signs of the numbers we're looking for are different from each other lead us to the conclusion that the only possibility for the two numbers we're looking for is:

$\begin{cases} m=5\\ n=-4 \end{cases}$

Therefore we'll factorize the given expression to:

$x^2+x-20 \\ \downarrow\\ (x+5)(x-4)$

Evidently the suggested factorization in the problem is incorrect.

Therefore - the correct answer is answer B.

Note:

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

$(x+2)(x-10)$(using the expanded distributive property), and checking if it indeed equals the given expression:

$x^2+x-20$, It is of course preferable to try to factorize the given expression - for practice purposes.