## Algebra: A Combined Approach (4th Edition)

Perimeter = $2x^{2}$ + 28x + 66 Perimeter factorized: 2( x + 11) (x + 3).
The perimeter of a rectangle = 2( length + breadth). length = $x^{2}$ + 10x breadth = 4x + 33 Thus the perimeter = 2( $x^{2}$ + 10x + 4x + 33) = $2x^{2}$ + 28x + 66. To factor $2x^{2}$ + 28x + 66, take out the Greatest Common Divisor first ( GCD = 2). Thus, $2x^{2}$ + 28x + 66 = 2($x^{2}$ + 14x + 33). Now, we need two numbers such that their sum is 14 and product is 33. Those numbers are 11 and 3. Thus complete factorization is 2( x + 11) (x + 3).