Question

1. 10n² - 67n + 42

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(10\times42 = 420\) and add up to \(-67\). The numbers are \(-60\) and \(-7\) since \((-60)\times(-7)=420\) and \(-60 + (-7)=-67\).

Step2: Rewrite the middle term

Rewrite \(-67n\) as \(-60n - 7n\) in the quadratic expression:
\(10n^{2}-60n - 7n + 42\)

Step3: Group the terms

Group the first two terms and the last two terms:
\((10n^{2}-60n)+(-7n + 42)\)

Step4: Factor out the GCF from each group

Factor out \(10n\) from the first group and \(-7\) from the second group:
\(10n(n - 6)-7(n - 6)\)

Step5: Factor out the common binomial factor

Factor out \((n - 6)\) from both terms:
\((10n - 7)(n - 6)\)

Answer:

\((10n - 7)(n - 6)\)