Question

factor completely.
$5p^2 - 5p - 30$
(there is a submit button and an input box in the image, but the main problem text is the factoring task of the quadratic expression.)

Explanation:

Step1: Find the GCF

The given expression is \(5p^2 - 5p - 30\). First, find the greatest common factor (GCF) of the three terms. The GCF of \(5\), \(-5\), and \(-30\) is \(5\).
\[5p^2 - 5p - 30 = 5(p^2 - p - 6)\]

Step2: Factor the quadratic

Now factor the quadratic \(p^2 - p - 6\). We need two numbers that multiply to \(-6\) and add to \(-1\). The numbers are \(-3\) and \(2\) because \((-3)\times2=-6\) and \(-3 + 2=-1\).
\[p^2 - p - 6=(p - 3)(p + 2)\]

Step3: Combine the factors

Substitute the factored quadratic back into the expression from Step 1.
\[5p^2 - 5p - 30 = 5(p - 3)(p + 2)\]

Answer:

\(5(p - 3)(p + 2)\)