Answer: \(GCF = p^2\)
Explanation:
To find the greatest common factor (GCF) of the expression \(4p^4 - 7p^3 - 3p^2\), we need to identify the highest power of \(p\) that divides all the terms evenly.
First, let's factor out the common term \(p^2\) from all the terms:
\(4p^4 - 7p^3 - 3p^2 = p^2(4p^2 - 7p - 3)\)
Now, let's factor the quadratic expression \(4p^2 - 7p - 3\) further:
\(4p^2 - 7p - 3 = (4p + 1)(p - 3)\)
So, we have factored the original expression as:
\(4p^4 - 7p^3 - 3p^2 = p^2(4p + 1)(p - 3)\)
Now, let's find the GCF of this factored expression. The GCF is the product of the common factors in each term, which are \(p^2\) and \(1\). Therefore, the GCF is:
\(GCF = p^2\)