Question

1. the area of a rectangle is given by the trinomial n² - 3n - 28. what are the possible dimensions of the rectangle? use factoring. a. n + 7 and n - 4 b. n - 7 and n + 4 c. n - 2 and n - 14 d. n + 2 and n + 14

Explanation:

Step1: Factor the trinomial

We need to factor \(n^{2}-3n - 28\). We look for two numbers that multiply to \(-28\) and add up to \(-3\). The numbers are \(-7\) and \(4\) since \((-7)\times4=-28\) and \(-7 + 4=-3\). So, \(n^{2}-3n - 28=n^{2}-7n+4n - 28\).

Step2: Group - factor

Group the terms: \((n^{2}-7n)+(4n - 28)=n(n - 7)+4(n - 7)=(n - 7)(n + 4)\)

Answer:

B. \(n - 7\) and \(n + 4\)