What is the factored form of the following expressions 16 x2

What is the factored form of the following expressions? 16- x2 - lOxy + 24/ 0(x + 6y)(x + 4y) O (x - 2y)(x + 12y) O (x + 2y)(x - 12y) O (x - 6y)(x - 4v) 17A ¢ The area of a rectangular barnyard is given by the trinomial 6x^ + 7x - 20. What are the possible dimensions of the barnyard? Use factoring. O 2x - 5 and 3x + 4 0-2x + 5 and-3x + 4 O 2x + 5 and 3x - 4 Ozx-5 and 3x-4

Solution

16. x² - 10xy + 24y² = x² - 6xy - 4xy + 24y² = x (x - 6y) - 4y( x - 6y) = (x - 6y) (x - 4y). The last answer is correct.

17. 6x² + 7x - 20 = 6x² - 8x + 15x - 20 = 2x( 3x -4) + 5( 3x - 4) = (2x + 5)( 3x -4) . Since the area of a rectangle is the product of its sides, the dimensions of the barnyard are 2x + 5 and 3x -4. The 3rd answer is correct.