Suppose $7x$ is split as $2x + 5x$; can a similar rectangular arrangement be formed?
Consider other possibilities and check.                                                                                                              [Page No. 79]

To factor $x^2 + 7x + 12$, the middle term $7x$ must be split into two terms whose coefficients add to $7$ and multiply to $12$ (the constant term).
Possible splits of $7$ are:
$1 + 6$, with product $1 \times 6 = 6$
$2 + 5$, with product $2 \times 5 = 10$
$3 + 4$, with product $3 \times 4 = 12$
Only $3$ and $4$ satisfy both conditions. Therefore,
$x^2 + 7x + 12 = x^2 + 3x + 4x + 12$
and the tiles can be arranged to form the rectangle $(x + 3)(x + 4)$.
Thus, the correct split is $3x + 4x$ because $3 \times 4 = 12$, matching the constant term.