Question

What are U and V in the factored expression 16x^4y^7 - 6x^5y^5?

A) U = 10x^4y^5, V = 8y^2
B) U = 8x^3y^4, V = 6x^2
C) U = 2x^4y^5, V = 6x^5y^2
D) U = 16x^3y^4, V = -6x^2y^5

Answer 1

The GCF of 16x^4y^7 and 6x^5y^5 is 2x^4y^5, which leads to the factored expression U(8y^2 - 3x), with U being 2x^4y^5 and V being 8y^2 - 3x.

Step-by-step explanation:

The student is asking about factoring algebraic expressions. To find U and V in the factored expression 16x^4y^7 - 6x^5y^5, we need to extract the greatest common factor (GCF) from both terms. The GCF of these two terms is 2x^4y^5, as it is the highest power of both x and y that divides each term completely. If we factor out the GCF, we get:

2x^4y^5(8y^2 - 3x)

So, the correct answer is:

• U = 2x^4y^5
• V = 8y^2 - 3x

Note that the answer choices provided may have a typo, as they do not present the subtracted term within V; none of the given choices encapsulate the complete factored form with both U and V properly defined.