Verify the Factorization: Is x^2+2x+1 = (x+2)(x-1)?

Use trinomial factoring to breakdown the given expression:

$x^2+2x+1$

Look for a pair of numbers whose product is the free term in the expression, and their sum is the coefficient of the first power term in the expression, meaning two numbers $m,\hspace{2pt}n$ that satisfy:

$m\cdot n=1\\ m+n=2\\$From the first requirement mentioned, namely - from the multiplication, note that the product of the numbers we're looking for needs to yield a positive result. Therefore we can conclude that both numbers have the same signs, according to the multiplication rules. The possible factors of 1 are 1 and -1. Fulfilling the second requirement mentioned, along with the fact that the signs of the numbers we're looking for are equal to each other lead us to the conclusion that the only possibility for the two numbers we're looking for is:

$\begin{cases} m=1\\ n=1\end{cases}$

Hence we'll factor the given expression to:

$x^2+2x+1 \\ \downarrow\\ (x+1)(x+1)$

The factorization suggested 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:

$(x+2)(x-1)$ (using the expanded distributive property), and checking if we indeed obtain the given expression:

$x^2+2x+1$, However it is of course preferable to try to factor the given expression - for practice purposes.