To find the greatest common factor (GCF) of the expression \( 4x^2y^5 + 10x^3y^4 \), we need to analyze the coefficients and the variables in each term.
- The coefficients are 4 and 10. The GCF of 4 and 10 is 2.
- For the variable \( x \), the lowest power between \( x^2 \) (from the first term) and \( x^3 \) (from the second term) is \( x^2 \).
- For the variable \( y \), the lowest power between \( y^5 \) (from the first term) and \( y^4 \) (from the second term) is \( y^4 \).
Now we can multiply the GCF components together:
- Coefficient: 2
- Variable \( x \): \( x^2 \)
- Variable \( y \): \( y^4 \)
Thus, the GCF is:
\[ 2x^2y^4 \]
Since none of the options you provided exactly match this GCF, it seems there may have been a misunderstanding in selection. However, 2xy (option 4 from your list, if interpreted from exponents to the base level) would contribute towards obtaining the correct factorization value, while 10x³ y5 would be too high based on lowest exponents.
Please double-check your interpretations or context clues given in your options related to the expression.
1 answer