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When factoring the expression

4x2y5+10x3y4


you determine that the greatest common factor is:

(1 point)
Responses

2x2y4
2 x squared y to the 4th power

10x3y5
10 x cubed y to the 5th power

4xy
4 x y

14x5y9

1 answer

To factor the expression \( 4x^2y^5 + 10x^3y^4 \), we first need to determine the greatest common factor (GCF) of the coefficients and the variables.

  1. Coefficients: The coefficients are 4 and 10.

    • The GCF of 4 and 10 is 2.

  2. Variables:

    • For \( x^2 \) and \( x^3 \), the GCF is \( x^2 \) (the lowest power).
    • For \( y^5 \) and \( y^4 \), the GCF is \( y^4 \) (the lowest power).

Now we can combine these:

  • GCF = \( 2x^2y^4 \).

Thus, the greatest common factor for the expression \( 4x^2y^5 + 10x^3y^4 \) is:

2x²y⁴ (or written as "2 x squared y to the 4th power").