Question

1. $p^2 - 14p + 40$

Explanation:

Step1: Find two numbers

Find two numbers that multiply to \(40\) and add up to \(-14\) (since the middle term is \(-14p\) and the constant term is \(40\)). The numbers are \(-4\) and \(-10\) because \((-4)\times(-10) = 40\) and \((-4)+(-10)=-14\).

Step2: Factor the quadratic

Rewrite the middle term using the two numbers: \(p^{2}-4p - 10p+40\). Then, group the terms: \((p^{2}-4p)+(-10p + 40)\). Factor out the greatest common factor from each group: \(p(p - 4)-10(p - 4)\). Finally, factor out the common binomial factor \((p - 4)\): \((p - 4)(p - 10)\).

Answer:

\((p - 4)(p - 10)\)