Factor completely. Always begin by factoring the GCF.
ax(squared)p-8pa-2axp
Please don't change names with each post. Six posts -- six different names
The GCF is ap.
ax^2 p-8pa-2axp = ap(x^2 -2x -8)
The expression in parentheses can be easily factored.
Take it from there
To factor the given expression completely, let's first look for the greatest common factor (GCF) of the terms.
The GCF is the largest expression that divides evenly into each term. In this case, the GCF is "a" since it is a common factor of all three terms:
a * x^2 * p - 8 * p * a - 2 * a * x * p
Now, we can factor out the GCF "a" from each term:
a(x^2 * p) - 8(p * a) - 2(x * p * a)
Simplifying further, we get:
a * (x^2 * p - 8 * a - 2 * x * p)
Now, let's focus on the expression inside the parentheses:
x^2 * p - 8 * a - 2 * x * p
We have two terms that contain the variable "x" and two terms that contain the variable "p." To factor this completely, we need to look for common factors among these terms.
Let's first group the terms in pairs:
(x^2 * p) - (8 * a) - (2 * x * p)
Now, let's identify common factors within each pair:
(x * x * p) - (2 * 2 * a) - (2 * x * p)
Simplifying further, we get:
(xp * x) - (4a * 2) - (2 * xp * 1)
Notice that "xp" is a common factor in all three terms. Let's factor it out:
xp * (x - 4a - 2)
Finally, we have factored the expression completely. The factored form is:
a * xp * (x - 4a - 2)