Question

When factoring the expression
4x²y 5 + 10x³y4
you determine that the greatest common factor is:
(1 point)
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О
10x³ y5
14x5y9
4
2x² y¹
4xy

Answer 1

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.

1. The coefficients are 4 and 10. The GCF of 4 and 10 is 2.
2. For the variable \( x \), the lowest power between \( x^2 \) (from the first term) and \( x^3 \) (from the second term) is \( x^2 \).
3. 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.