Question
When factoring the expression 4x^2y^5 + 10x^3y^4 you determine that the greatest common factor is:
A) 10x^3y^5
B) 4xy
C) 2x^2y^4
D) 14x^5y^9
A) 10x^3y^5
B) 4xy
C) 2x^2y^4
D) 14x^5y^9
Answers
GPT-4o mini
To find the greatest common factor (GCF) of the expression \(4x^2y^5 + 10x^3y^4\), we need to identify the GCF of the coefficients and the variables in each term.
1. **Coefficients:**
- The coefficients are \(4\) and \(10\).
- The GCF of \(4\) and \(10\) is \(2\).
2. **Variable \(x\):**
- The powers of \(x\) are \(x^2\) and \(x^3\).
- The GCF is \(x^{\min(2, 3)} = x^2\).
3. **Variable \(y\):**
- The powers of \(y\) are \(y^5\) and \(y^4\).
- The GCF is \(y^{\min(5, 4)} = y^4\).
Putting it all together, the GCF of \(4x^2y^5\) and \(10x^3y^4\) is:
\[
2x^2y^4
\]
Thus, the correct answer is:
C) \(2x^2y^4\)
1. **Coefficients:**
- The coefficients are \(4\) and \(10\).
- The GCF of \(4\) and \(10\) is \(2\).
2. **Variable \(x\):**
- The powers of \(x\) are \(x^2\) and \(x^3\).
- The GCF is \(x^{\min(2, 3)} = x^2\).
3. **Variable \(y\):**
- The powers of \(y\) are \(y^5\) and \(y^4\).
- The GCF is \(y^{\min(5, 4)} = y^4\).
Putting it all together, the GCF of \(4x^2y^5\) and \(10x^3y^4\) is:
\[
2x^2y^4
\]
Thus, the correct answer is:
C) \(2x^2y^4\)