Question

1. $9n^2 + 21n - 8$

Explanation:

Step1: Find two numbers that multiply to \(9\times(-8)= -72\) and add to \(21\).

The numbers are \(24\) and \(-3\) since \(24\times(-3)= -72\) and \(24 + (-3)=21\).

Step2: Rewrite the middle term using these numbers.

\(9n^{2}+24n - 3n - 8\)

Step3: Group the first two and last two terms.

\((9n^{2}+24n)+(-3n - 8)\)

Step4: Factor out the greatest common factor from each group.

\(3n(3n + 8)-1(3n + 8)\)

Step5: Factor out the common binomial factor.

\((3n + 8)(3n - 1)\)

Answer:

\((3n + 8)(3n - 1)\)