To determine the Greatest Common Factor (GCF) of the expression [tex]\(25 x^2 - 5 x\)[/tex], we need to find the largest factor that can be factored out from each term of the expression.
1. Identify the individual terms in the expression:
The expression is [tex]\(25 x^2 - 5 x\)[/tex]. The terms are [tex]\(25 x^2\)[/tex] and [tex]\(-5 x\)[/tex].
2. Determine the factors of each coefficient:
- The coefficient of the first term [tex]\(25 x^2\)[/tex] is 25. The factors of 25 are [tex]\(1, 5, 25\)[/tex].
- The coefficient of the second term [tex]\(-5 x\)[/tex] is [tex]\(-5\)[/tex]. The factors of [tex]\(-5\)[/tex] are [tex]\(1, -1, 5, -5\)[/tex].
3. Find the Greatest Common Factor of the numerical coefficients:
The highest common factor of the numbers 25 and [tex]\(-5\)[/tex] is 5.
4. Look for common factors in the variable part:
The variable part of the first term is [tex]\(x^2\)[/tex] and of the second term is [tex]\(x\)[/tex]. The common variable factor with the lowest power is [tex]\(x\)[/tex].
5. Combine the common numerical and variable factors:
The GCF combines the numerical factor and the variable factor found in both terms.
So, combining 5 and [tex]\(x\)[/tex], we get [tex]\(5x\)[/tex].
Therefore, the GCF of the expression [tex]\(25 x^2 - 5 x\)[/tex] is [tex]\(5 x\)[/tex].
The correct answer is:
(A) [tex]\(5 x\)[/tex].
