The expression you provided is a quadratic equation:

\[
v^2 - 12v + 35
\]

To solve or factor this, we can attempt to factor the quadratic expression. We're looking for two numbers that multiply to give 35 and add to give -12.

Those two numbers are -5 and -7 because:
\[
(-5) \times (-7) = 35
\]
\[
(-5) + (-7) = -12
\]

Thus, the factored form of the quadratic expression is:

\[
(v - 5)(v - 7)
\]

This is the factored form of \( v^2 - 12v + 35 \).

Would you like to solve for \(v\) or get more details on the factorization process?

### Related Questions:
1. What are the steps to solve quadratic equations by factoring?
2. How do you use the quadratic formula for solving this equation?
3. Can all quadratic equations be factored?
4. What is the significance of the roots \(v = 5\) and \(v = 7\)?
5. How does completing the square work on \(v^2 - 12v + 35\)?

**Tip:** Always check if a quadratic expression can be factored before using other methods like the quadratic formula. This can save time!

Learn how to factor the quadratic equation v²−12v+35 by finding two numbers that multiply to give 35 and add to give -12. This detailed solution covers essential algebraic concepts, including factoring and the Zero Product Property. Suitable for students in Grades 8-10.

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