#### Answer

Perimeter = $2x^{2}$ + 28x + 66
Perimeter factorized: 2( x + 11) (x + 3).

#### Work Step by Step

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).