To factor out the Greatest Common Factor (GCF) from the expression [tex]\(5xy - 2y\)[/tex], follow these steps:
1. Identify the Terms: The given expression is [tex]\(5xy - 2y\)[/tex]. It contains two terms: [tex]\(5xy\)[/tex] and [tex]\(-2y\)[/tex].
2. Find the GCF: The GCF is the largest factor common to each term.
- The term [tex]\(5xy\)[/tex] includes the factors 5, [tex]\(x\)[/tex], and [tex]\(y\)[/tex].
- The term [tex]\(-2y\)[/tex] includes the factors -2 and [tex]\(y\)[/tex].
- The common factor in both terms is [tex]\(y\)[/tex].
3. Factor Out the GCF: Once the GCF is determined, you factor it out of each term:
- Divide [tex]\(5xy\)[/tex] by [tex]\(y\)[/tex] which leaves you with [tex]\(5x\)[/tex].
- Divide [tex]\(-2y\)[/tex] by [tex]\(y\)[/tex] which leaves you with [tex]\(-2\)[/tex].
4. Write the Factored Expression: Place the GCF in front of a parenthesis, and inside the parenthesis, put the simplified terms resulting from the division:
[tex]\[
y (5x - 2)
\][/tex]
Thus, the expression [tex]\(5xy - 2y\)[/tex] factored out using the GCF is [tex]\(y (5x - 2)\)[/tex].
So, the correct answer is:
[tex]\[
y(5x - 2)
\][/tex]
Here are the incorrect options explained:
- [tex]\(xy(5 - 2y)\)[/tex] is incorrect because it does not properly factor out the GCF and modifies the expression incorrectly.
- [tex]\(5(xy - 2)\)[/tex] is incorrect because 5 is not a common factor of both terms.
- [tex]\(2(5x - y)\)[/tex] is incorrect because 2 is not a common factor of both terms.
Therefore, the correctly factored form is [tex]\(y(5x - 2)\)[/tex].
