To tackle the problem, we need to understand the provided expression and identify the method used to simplify it. The given expression is [tex]\((x^2 - 2)(-5x^2 + x)\)[/tex].
First, let's rewrite it:
[tex]\[
(x^2 - 2)(-5x^2 + x)
\][/tex]
We have a product of two binomials, and it is simplified using the method outlined in the question:
[tex]\[
(x^2)(-5x^2) + (x^2)(x) + (-2)(-5x^2) + (-2)(x)
\][/tex]
Each term in the first binomial [tex]\(x^2 - 2\)[/tex] is multiplied by each term in the second binomial [tex]\(-5x^2 + x\)[/tex]. Let's analyze the terms one-by-one:
1. First Terms:
[tex]\[
(x^2)(-5x^2) = -5x^4
\][/tex]
2. Outer Terms:
[tex]\[
(x^2)(x) = x^3
\][/tex]
3. Inner Terms:
[tex]\[
(-2)(-5x^2) = 10x^2
\][/tex]
4. Last Terms:
[tex]\[
(-2)(x) = -2x
\][/tex]
By observing the multiplication pattern, we see that it follows the steps First, Outer, Inner, Last. This is a classic example of the FOIL method used for multiplying binomials.
Thus, the correct answer is:
[tex]\[
\boxed{\text{C. FOIL}}
\][/tex]
