Algebra: A Combined Approach (4th Edition)

Published by Pearson

Chapter 6 - Section 6.2 - Factoring Trinomials of the Form x2+bx+c - Exercise Set - Page 430: 81

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).

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