Question

Factor (y² + 10z - 10y - yz).

1. ((z - y)(y - 10))
2. ((y - z)(y - 10))
3. ((y - z)(10 - y))
4. None of the above

Answer 1

After rearranging and factoring common terms, the correct factorization of the polynomial expression (y² + 10z - 10y - yz) is (y - z)(y - 10), which is option 2 in the provided choices.

Step-by-step explanation:

To factor the given polynomial expression (y² + 10z - 10y - yz), we need to group terms in a way that allows us to use the distributive property. We look for terms that have a common factor, and we arrange them accordingly. After rearranging, we have:

(y² - yz) + (10z - 10y)

First, we factor out a y from the first group and a 10 from the second group:

y(y - z) + 10(z - y)

Noticing that (y - z) and (z - y) are opposites, we can factor out (y - z) as a common factor:

(y - z)(y - 10)

The correct factorization of the expression is therefore (y - z)(y - 10), which corresponds to option 2 in the multiple-choice list.