Question

The area of a rectangle is 6x^2-9x-15. And the length is (2x-5). Which expression best represents the rectangle’s width?

Answer 1

The area of the rectangle is of the form 6x² - 9x - 15

Factoring the given expression,

`\sf \: {6x}^(2) - 9x - 15 \\ \\ \leadsto \: \sf \: 3\bigg( {2x}^(2) - 3x - 5 \bigg) \\ \\ \leadsto \: \sf \: 3 \bigg( {2x}^(2) - 5x + 2x - 5 \bigg) \\ \\ \leadsto \: \sf \: 3 \bigg((2x - 5)(x + 1) \bigg)`

Length of the rectangle is 2x - 5

Thus,

`\leadsto \: \sf \: (2x - 5)(3x + 3)`

The breadth of the rectangle is 3x + 3