Question

1. (2n^2 - 3n - 27)

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times(-27)= - 54\) and add up to \(-3\). The numbers are \(-9\) and \(6\) since \(-9\times6=-54\) and \(-9 + 6=-3\).

Step2: Split the middle term

Rewrite the middle term \(-3n\) as \(-9n+6n\) in the quadratic expression:
\(2n^{2}-9n + 6n-27\)

Step3: Group the terms

Group the first two terms and the last two terms:
\((2n^{2}-9n)+(6n - 27)\)

Step4: Factor out the GCF from each group

Factor out \(n\) from the first group and \(3\) from the second group:
\(n(2n - 9)+3(2n - 9)\)

Step5: Factor out the common binomial factor

Factor out \((2n - 9)\) from the expression:
\((2n - 9)(n + 3)\)

Answer:

\((2n - 9)(n + 3)\)