Question

factor completely: (2t^2 - 40t - 42)

Explanation:

Step1: Identify the GCF

First, find the greatest common factor (GCF) of the terms \(2t^2\), \(-40t\), and \(-42\). The GCF of 2, 40, and 42 is 2.
\[
2t^2 - 40t - 42 = 2(t^2 - 20t - 21)
\]

Step2: Factor the quadratic

Now, factor the quadratic \(t^2 - 20t - 21\). We need two numbers that multiply to \(-21\) and add to \(-20\). Those numbers are \(-21\) and \(1\).
\[
t^2 - 20t - 21 = (t - 21)(t + 1)
\]

Step3: Combine the factors

Putting it all together, the completely factored form is:
\[
2(t - 21)(t + 1)
\]

Answer:

\(2(t - 21)(t + 1)\)