Algebra tiles can be used to represent products and find factors.
(A) Figure out the product of $x + 2$ and $x + 3$ using algebra tiles.
(B) Lay out algebra tiles for $x^{2} + 11x + 30$ in such a way that you will see its factors.                    [Page No. 79]

(A) $(x + 2)(x + 3)$

Arrange algebra tiles to form a rectangle with sides $(x + 2)$ and $(x + 3)$.

$1x^2$-tile

5x-tiles (2 along one side and 3 along the other)

6 unit tiles arranged in a $2 \times 3$ block

The total area is $x^2 + 5x + 6$.

Hence, $(x + 2)(x + 3) = x^2 + 5x + 6$.

(B) To factor the expression, split $11x$ into two terms whose coefficients add to 11 and multiply to 30.

$5 + 6 = 11, 5 \times 6 = 30$.

Thus, $x^2 + 11x + 30 = x^2 + 5x + 6x + 30$.

Using algebra tiles, arrange:

$1x^2$-tile

11 $x$-tiles (5 on one side and 6 on the other) 
30 unit tiles in a $5 \times 6$ rectangle

The completed rectangle has dimensions $(x + 5)$ and $(x + 6)$.

Therefore, $x^2 + 11x + 30 = (x + 5)(x + 6)$.