Question

1. $7x^2 - 69x - 10$

Explanation:

Step1: Find two numbers that multiply to \(7\times(-10) = -70\) and add up to \(-69\).

The numbers are \(-70\) and \(1\) since \(-70\times1=-70\) and \(-70 + 1=-69\).

Step2: Rewrite the middle term using these two numbers.

\(7x^{2}-70x + x-10\)

Step3: Group the terms and factor out the greatest common factor (GCF) from each group.

\((7x^{2}-70x)+(x - 10)=7x(x - 10)+1(x - 10)\)

Step4: Factor out the common binomial factor \((x - 10)\).

\((7x + 1)(x - 10)\)

Answer:

\((7x + 1)(x - 10)\)