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The question is asking for the other factor of the quadratic expression \( y^2 - 10y + 16 \), given that one of its factors is \( y - 2 \).

To find the other factor, we can use polynomial division or factoring techniques. Here’s a step-by-step solution using factoring:

1. Since \( y - 2 \) is a factor, we know that:
   \[
   y^2 - 10y + 16 = (y - 2)(y - b)
   \]
   where \( b \) is some constant we need to find.

2. Expanding \( (y - 2)(y - b) \) gives:
   \[
   y^2 - (2 + b)y + 2b
   \]

3. By comparing coefficients with \( y^2 - 10y + 16 \):
   - For the \( y \)-term: \( -(2 + b) = -10 \), so \( 2 + b = 10 \), giving \( b = 8 \).
   - For the constant term: \( 2b = 16 \), which also confirms \( b = 8 \).

4. Thus, the other factor is \( y - 8 \).

### Answer
The correct option is:
- \( y - 8 \)

Would you like more details on this factorization or have any questions?

### Additional Related Questions
1. How can we check if a binomial is a factor of a polynomial?
2. What other methods can we use to factorize quadratic expressions?
3. How would the solution change if the polynomial was \( y^2 - 10y + 20 \)?
4. What is the remainder theorem and how can it help in finding factors?
5. Can a quadratic expression have complex factors? If so, how are they identified?

### Tip
When factoring a quadratic expression, always check the discriminant first. It can help you determine if the expression has real, rational, or complex roots.

The binomial (y - 2) is a factor of y^2 - 10y + 16. What is the other factor?

Learn how to find the other factor of the quadratic expression y^2 - 10y + 16 given one factor (y - 2). This problem involves factoring techniques and the Factor Theorem, suitable for students in Grades 8-10.

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